Mister Exam
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- Equation x^2+76x+915=0
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- x^ two +76x+ nine hundred and fifteen = zero
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Similar expressions
- x^2-76x+915=0
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x^2+76x+915=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
$$a = 1$$
$$b = 76$$
$$c = 915$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -15$$
$$x_{2} = -61$$
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
$$a = 1$$
$$b = 76$$
$$c = 915$$
, then
D = b^2 - 4 * a * c =
(76)^2 - 4 * (1) * (915) = 2116
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -15$$
$$x_{2} = -61$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 76$$
$$q = \frac{c}{a}$$
$$q = 915$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -76$$
$$x_{1} x_{2} = 915$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 76$$
$$q = \frac{c}{a}$$
$$q = 915$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -76$$
$$x_{1} x_{2} = 915$$
Sum and product of roots
[src]
sum
-61 - 15
$$-61 - 15$$
=
-76
$$-76$$
product
-61*(-15)
$$- -915$$
=
915
$$915$$
915