Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 7*x=0
-
Equation 3x-2=x+4
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Equation tan(x)=7
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Equation (x-3)(x^2-2x+1)=3(x-1)
- Express {x} in terms of y where:
- 18*x-10*y=-9
- 18*x-12*y=-9
- 12*x+11*y=20
- 19*x-12*y=-9
- Factor squared:
- x^2-x-8
-
Identical expressions
- x^ two -x- eight = zero
- x squared minus x minus 8 equally 0
- x to the power of two minus x minus eight equally zero
- x2-x-8=0
- x²-x-8=0
- x to the power of 2-x-8=0
- x^2-x-8=O
-
Similar expressions
- x^2+x-8=0
- x^2-x+8=0
x^2-x-8=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
$$a = 1$$
$$b = -1$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{1}{2} + \frac{\sqrt{33}}{2}$$
$$x_{2} = \frac{1}{2} - \frac{\sqrt{33}}{2}$$
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
$$a = 1$$
$$b = -1$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-8) = 33
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{1}{2} + \frac{\sqrt{33}}{2}$$
$$x_{2} = \frac{1}{2} - \frac{\sqrt{33}}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -8$$
Sum and product of roots
[src]
sum
____ ____ 1 \/ 33 1 \/ 33 - - ------ + - + ------ 2 2 2 2
$$\left(\frac{1}{2} - \frac{\sqrt{33}}{2}\right) + \left(\frac{1}{2} + \frac{\sqrt{33}}{2}\right)$$
=
1
$$1$$
product
/ ____\ / ____\ |1 \/ 33 | |1 \/ 33 | |- - ------|*|- + ------| \2 2 / \2 2 /
$$\left(\frac{1}{2} - \frac{\sqrt{33}}{2}\right) \left(\frac{1}{2} + \frac{\sqrt{33}}{2}\right)$$
=
-8
$$-8$$
-8
Rapid solution
[src]
____
1 \/ 33
x1 = - - ------
2 2
$$x_{1} = \frac{1}{2} - \frac{\sqrt{33}}{2}$$
____
1 \/ 33
x2 = - + ------
2 2
$$x_{2} = \frac{1}{2} + \frac{\sqrt{33}}{2}$$
x2 = 1/2 + sqrt(33)/2
The graph