Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 4^x=8
-
Equation x-5(x+3)=5
-
Equation -x=2
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Equation x^2-8=0
- Express {x} in terms of y where:
- -7*x-13*y=-12
- 8*x+1*y=4
- 20*x-16*y=7
- -3*x+19*y=16
- Derivative of:
- x^2-8
- Factor polynomial:
- x^2-8
-
Identical expressions
- x^ two - eight = zero
- x squared minus 8 equally 0
- x to the power of two minus eight equally zero
- x2-8=0
- x²-8=0
- x to the power of 2-8=0
- x^2-8=O
-
Similar expressions
- x^2+8=0
x^2-8=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
$$a = 1$$
$$b = 0$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2}$$
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
$$a = 1$$
$$b = 0$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-8) = 32
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 \sqrt{2}$$
$$x_{2} = - 2 \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -8$$
Rapid solution
[src]
___ x1 = -2*\/ 2
$$x_{1} = - 2 \sqrt{2}$$
___ x2 = 2*\/ 2
$$x_{2} = 2 \sqrt{2}$$
x2 = 2*sqrt(2)
Sum and product of roots
[src]
sum
___ ___ - 2*\/ 2 + 2*\/ 2
$$- 2 \sqrt{2} + 2 \sqrt{2}$$
=
0
$$0$$
product
___ ___ -2*\/ 2 *2*\/ 2
$$- 2 \sqrt{2} \cdot 2 \sqrt{2}$$
=
-8
$$-8$$
-8
The graph