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- x^2-8*x-12=0
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x^2+8*x-12=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
$$a = 1$$
$$b = 8$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4 + 2 \sqrt{7}$$
$$x_{2} = - 2 \sqrt{7} - 4$$
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
$$a = 1$$
$$b = 8$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (1) * (-12) = 112
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4 + 2 \sqrt{7}$$
$$x_{2} = - 2 \sqrt{7} - 4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = -12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = -12$$
Rapid solution
[src]
___ x1 = -4 + 2*\/ 7
$$x_{1} = -4 + 2 \sqrt{7}$$
___ x2 = -4 - 2*\/ 7
$$x_{2} = - 2 \sqrt{7} - 4$$
x2 = -2*sqrt(7) - 4
Sum and product of roots
[src]
sum
___ ___ -4 + 2*\/ 7 + -4 - 2*\/ 7
$$\left(- 2 \sqrt{7} - 4\right) + \left(-4 + 2 \sqrt{7}\right)$$
=
-8
$$-8$$
product
/ ___\ / ___\ \-4 + 2*\/ 7 /*\-4 - 2*\/ 7 /
$$\left(-4 + 2 \sqrt{7}\right) \left(- 2 \sqrt{7} - 4\right)$$
=
-12
$$-12$$
-12
The graph