Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-1)*(x^2+8*x+16)=6*(x+4)
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Equation 2*(-4*x^2/(x^2-4)+1+(x^2+4)*(4*x^2/(x^2-4)-1)/(x^2-4))/(x^2-4)=0
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Equation 4(x+6)=x
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Equation x^2-5*x-1=0
- Express {x} in terms of y where:
- 11*x-2*y=9
- 17*x+14*y=6
- -18*x-1*y=-12
- -1*x+18*y=-13
- Graphing y =:
- x^2-5*x-1
-
Identical expressions
- x^ two - five *x- one = zero
- x squared minus 5 multiply by x minus 1 equally 0
- x to the power of two minus five multiply by x minus one equally zero
- x2-5*x-1=0
- x²-5*x-1=0
- x to the power of 2-5*x-1=0
- x^2-5x-1=0
- x2-5x-1=0
- x^2-5*x-1=O
-
Similar expressions
- x^2+5*x-1=0
- x^2-5*x+1=0
x^2-5*x-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = -5$$
$$c = -1$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{5}{2} + \frac{\sqrt{29}}{2}$$
$$x_{2} = \frac{5}{2} - \frac{\sqrt{29}}{2}$$
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
$$a = 1$$
$$b = -5$$
$$c = -1$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (-1) = 29
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{2} + \frac{\sqrt{29}}{2}$$
$$x_{2} = \frac{5}{2} - \frac{\sqrt{29}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = -1$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -5$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 5$$
$$x_{1} x_{2} = -1$$
Sum and product of roots
[src]
sum
____ ____ 5 \/ 29 5 \/ 29 - - ------ + - + ------ 2 2 2 2
$$\left(\frac{5}{2} - \frac{\sqrt{29}}{2}\right) + \left(\frac{5}{2} + \frac{\sqrt{29}}{2}\right)$$
=
5
$$5$$
product
/ ____\ / ____\ |5 \/ 29 | |5 \/ 29 | |- - ------|*|- + ------| \2 2 / \2 2 /
$$\left(\frac{5}{2} - \frac{\sqrt{29}}{2}\right) \left(\frac{5}{2} + \frac{\sqrt{29}}{2}\right)$$
=
-1
$$-1$$
-1
Rapid solution
[src]
____
5 \/ 29
x1 = - - ------
2 2
$$x_{1} = \frac{5}{2} - \frac{\sqrt{29}}{2}$$
____
5 \/ 29
x2 = - + ------
2 2
$$x_{2} = \frac{5}{2} + \frac{\sqrt{29}}{2}$$
x2 = 5/2 + sqrt(29)/2
The graph