Mister Exam
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How to use it?
- Equation:
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Equation (x+6)^3=25*(x+6)
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Equation 1-5x=-6x+8
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Equation 1-5*x=-6*x+8
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Equation x^2-8*x+17=0
- Express {x} in terms of y where:
- -7*x-7*y=-14
- 10*x-2*y=0
- -15*x+17*y=13
- -11*x-15*y=14
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Identical expressions
- one *((x- two)*(x- three)*(x- four)*(x- five))/ twenty-four + thirteen *((x- one)*(x- three)*(x- four)*(x- five))/(- six)+ twenty-nine *((x- one)*(x- two)*(x- four)*(x- five))/ four + forty-nine *((x- one)*(x- two)*(x- three)*(x- five))/(- six)+ seventy-three *((x- one)*(x- two)*(x- three)*(x- four))/ twenty-four = zero
- 1 multiply by ((x minus 2) multiply by (x minus 3) multiply by (x minus 4) multiply by (x minus 5)) divide by 24 plus 13 multiply by ((x minus 1) multiply by (x minus 3) multiply by (x minus 4) multiply by (x minus 5)) divide by ( minus 6) plus 29 multiply by ((x minus 1) multiply by (x minus 2) multiply by (x minus 4) multiply by (x minus 5)) divide by 4 plus 49 multiply by ((x minus 1) multiply by (x minus 2) multiply by (x minus 3) multiply by (x minus 5)) divide by ( minus 6) plus 73 multiply by ((x minus 1) multiply by (x minus 2) multiply by (x minus 3) multiply by (x minus 4)) divide by 24 equally 0
- one multiply by ((x minus two) multiply by (x minus three) multiply by (x minus four) multiply by (x minus five)) divide by twenty minus four plus thirteen multiply by ((x minus one) multiply by (x minus three) multiply by (x minus four) multiply by (x minus five)) divide by ( minus six) plus twenty minus nine multiply by ((x minus one) multiply by (x minus two) multiply by (x minus four) multiply by (x minus five)) divide by four plus forty minus nine multiply by ((x minus one) multiply by (x minus two) multiply by (x minus three) multiply by (x minus five)) divide by ( minus six) plus seventy minus three multiply by ((x minus one) multiply by (x minus two) multiply by (x minus three) multiply by (x minus four)) divide by twenty minus four equally zero
- 1((x-2)(x-3)(x-4)(x-5))/24+13((x-1)(x-3)(x-4)(x-5))/(-6)+29((x-1)(x-2)(x-4)(x-5))/4+49((x-1)(x-2)(x-3)(x-5))/(-6)+73((x-1)(x-2)(x-3)(x-4))/24=0
- 1x-2x-3x-4x-5/24+13x-1x-3x-4x-5/-6+29x-1x-2x-4x-5/4+49x-1x-2x-3x-5/-6+73x-1x-2x-3x-4/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=O
- 1*((x-2)*(x-3)*(x-4)*(x-5)) divide by 24+13*((x-1)*(x-3)*(x-4)*(x-5)) divide by (-6)+29*((x-1)*(x-2)*(x-4)*(x-5)) divide by 4+49*((x-1)*(x-2)*(x-3)*(x-5)) divide by (-6)+73*((x-1)*(x-2)*(x-3)*(x-4)) divide by 24=0
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Similar expressions
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x+3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x+3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x+1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)-29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x+4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x+5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x+4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x+3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x+2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x+1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x+1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x+1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x+5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x+5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24-13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x+4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x+3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x+2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x+2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4-49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)-73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x+2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x+4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x+5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
- 1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0
1*((x-2)*(x-3)*(x-4)*(x-5))/24+13*((x-1)*(x-3)*(x-4)*(x-5))/(-6)+29*((x-1)*(x-2)*(x-4)*(x-5))/4+49*((x-1)*(x-2)*(x-3)*(x-5))/(-6)+73*((x-1)*(x-2)*(x-3)*(x-4))/24=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
(x - 2)*(x - 3)*(x - 4)*(x - 5) 13*(x - 1)*(x - 3)*(x - 4)*(x - 5) 29*(x - 1)*(x - 2)*(x - 4)*(x - 5) 49*(x - 1)*(x - 2)*(x - 3)*(x - 5) 73*(x - 1)*(x - 2)*(x - 3)*(x - 4)
------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- + ---------------------------------- = 0
24 -6 4 -6 24
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
Detail solution
Expand the expression in the equation
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
We get the quadratic equation
$$2 x^{2} + 6 x - 7 = 0$$
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 6$$
$$c = -7$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
$$\frac{73 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 4\right)}{24} + \left(\frac{49 \left(x - 2\right) \left(x - 1\right) \left(x - 3\right) \left(x - 5\right)}{-6} + \left(\frac{29 \left(x - 2\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{4} + \left(\frac{\left(x - 3\right) \left(x - 2\right) \left(x - 4\right) \left(x - 5\right)}{24} + \frac{13 \left(x - 3\right) \left(x - 1\right) \left(x - 4\right) \left(x - 5\right)}{-6}\right)\right)\right) = 0$$
We get the quadratic equation
$$2 x^{2} + 6 x - 7 = 0$$
This equation is of the form
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 2$$
$$b = 6$$
$$c = -7$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (2) * (-7) = 92
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
Rapid solution
[src]
____
3 \/ 23
x1 = - - + ------
2 2
$$x_{1} = - \frac{3}{2} + \frac{\sqrt{23}}{2}$$
____
3 \/ 23
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{23}}{2} - \frac{3}{2}$$
x2 = -sqrt(23)/2 - 3/2
Sum and product of roots
[src]
sum
____ ____ 3 \/ 23 3 \/ 23 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{23}}{2} - \frac{3}{2}\right) + \left(- \frac{3}{2} + \frac{\sqrt{23}}{2}\right)$$
=
-3
$$-3$$
product
/ ____\ / ____\ | 3 \/ 23 | | 3 \/ 23 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{3}{2} + \frac{\sqrt{23}}{2}\right) \left(- \frac{\sqrt{23}}{2} - \frac{3}{2}\right)$$
=
-7/2
$$- \frac{7}{2}$$
-7/2