Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-11)/(x-6)=11/16
-
Equation 5*x=12
-
Equation 2*sin(x)*cos(x)=0
-
Equation sqrt(x+1)-sqrt(4-x)+3=2*sqrt(4+3x-x^2)
- Express {x} in terms of y where:
- -20*x-7*y=-17
- -16*x-9*y=-5
- -8*x-11*y=1
- -7*x-16*y=8
-
Identical expressions
- (-x- thirteen)(-5x+ two)= zero
- ( minus x minus 13)( minus 5x plus 2) equally 0
- ( minus x minus thirteen)( minus 5x plus two) equally zero
- -x-13-5x+2=0
- (-x-13)(-5x+2)=O
-
Similar expressions
- (x-13)(-5x+2)=0
- (-x-13)(-5x-2)=0
- (-x-13)(5x+2)=0
- (-x+13)(-5x+2)=0
(-x-13)(-5x+2)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(2 - 5 x\right) \left(- x - 13\right) = 0$$
We get the quadratic equation
$$5 x^{2} + 63 x - 26 = 0$$
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
$$a = 5$$
$$b = 63$$
$$c = -26$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = -13$$
$$\left(2 - 5 x\right) \left(- x - 13\right) = 0$$
We get the quadratic equation
$$5 x^{2} + 63 x - 26 = 0$$
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
$$a = 5$$
$$b = 63$$
$$c = -26$$
, then
D = b^2 - 4 * a * c =
(63)^2 - 4 * (5) * (-26) = 4489
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = -13$$
Sum and product of roots
[src]
sum
-13 + 2/5
$$-13 + \frac{2}{5}$$
=
-63/5
$$- \frac{63}{5}$$
product
-13*2 ----- 5
$$- \frac{26}{5}$$
=
-26/5
$$- \frac{26}{5}$$
-26/5