Mister Exam

Other calculators


x^2+8*x+15=0

x^2+8*x+15=0 equation

The teacher will be very surprised to see your correct solution 😉

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src]
 2               
x  + 8*x + 15 = 0
$$\left(x^{2} + 8 x\right) + 15 = 0$$
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 - it is the discriminant.
Because
$$a = 1$$
$$b = 8$$
$$c = 15$$
, then
D = b^2 - 4 * a * c = 

(8)^2 - 4 * (1) * (15) = 4

Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = -3$$
$$x_{2} = -5$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = 15$$
The graph
Sum and product of roots [src]
sum
-5 - 3
$$-5 - 3$$
=
-8
$$-8$$
product
-5*(-3)
$$- -15$$
=
15
$$15$$
15
Rapid solution [src]
x1 = -5
$$x_{1} = -5$$
x2 = -3
$$x_{2} = -3$$
x2 = -3
Numerical answer [src]
x1 = -3.0
x2 = -5.0
x2 = -5.0
The graph
x^2+8*x+15=0 equation