Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x-y=2
-
Equation x^3+2x^2-x-2=0
- Equation (x+20)*(-x+10)=0
-
Equation x^2+8*x+15=0
- Express {x} in terms of y where:
- 15*x+7*y=2
- 12*x-20*y=10
- -17*x-15*y=-17
- 6*x-2*y=20
- Factor squared:
- x^2+8*x+15
-
Identical expressions
- x^ two + eight *x+ fifteen = zero
- x squared plus 8 multiply by x plus 15 equally 0
- x to the power of two plus eight multiply by x plus fifteen equally zero
- x2+8*x+15=0
- x²+8*x+15=0
- x to the power of 2+8*x+15=0
- x^2+8x+15=0
- x2+8x+15=0
- x^2+8*x+15=O
-
Similar expressions
- x^2+8*x-15=0
- x^2-8*x+15=0
x^2+8*x+15=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
$$a = 1$$
$$b = 8$$
$$c = 15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3$$
$$x_{2} = -5$$
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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = 15$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 8$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -8$$
$$x_{1} x_{2} = 15$$
Sum and product of roots
[src]
sum
-5 - 3
$$-5 - 3$$
=
-8
$$-8$$
product
-5*(-3)
$$- -15$$
=
15
$$15$$
15
The graph