Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2=-74
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Equation sqrt(5/15-x)=1
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Equation x^2+x-42=0
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Equation x^2-7x-8=0
- Express {x} in terms of y where:
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Identical expressions
- x^ two -7x- eight = zero
- x squared minus 7x minus 8 equally 0
- x to the power of two minus 7x minus eight equally zero
- x2-7x-8=0
- x²-7x-8=0
- x to the power of 2-7x-8=0
- x^2-7x-8=O
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Similar expressions
- x^2-7x+8=0
- x^2+7x-8=0
x^2-7x-8=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = -8$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \left(-8\right) + \left(-7\right)^{2} = 81$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 8$$
Simplify
$$x_{2} = -1$$
Simplify
$$a\ x^2 + b\ x + c = 0$$
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 $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 1$$
$$b = -7$$
$$c = -8$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 1 \cdot 4 \left(-8\right) + \left(-7\right)^{2} = 81$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 8$$
Simplify
$$x_{2} = -1$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = -8$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 7$$
$$x_{1} x_{2} = -8$$
Sum and product of roots
[src]
sum
-1 + 8
$$\left(-1\right) + \left(8\right)$$
=
7
$$7$$
product
-1 * 8
$$\left(-1\right) * \left(8\right)$$
=
-8
$$-8$$
The graph