# Use the discriminant to determine the number and type of solutions the equation has? x^2 + 8x + 12 = 0 A.no real solution B.one real solution C. two rational solutions D. two irrational solutions

Mar 13, 2016

C. two Rational solutions

#### Explanation:

The solution to the quadratic equation
$a \cdot {x}^{2} + b \cdot x + c = 0$ is
x = (-b+- sqrt (b^2 - 4*a*c )) / (2* a
In the problem under consideration,
a = 1, b = 8 and c = 12
Substituting,
x = (-8+- sqrt (8^2 - 4*1*12 )) / (2* 1
or x = (-8+- sqrt (64 - 48 )) / (2
x = (-8+- sqrt (16)) / (2
x = (-8+- 4) / (2
$x = \frac{- 8 + 4}{2} \mathmr{and} x = \frac{- 8 - 4}{2}$
$x = \frac{- 4}{2} \mathmr{and} x = \frac{- 12}{2}$
$x = - 2 \mathmr{and} x = - 6$