Question

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

Answer 1

C. two Rational solutions

Explanation:

The solution to the quadratic equation
`a*x^2 + b*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 = (-8 + 4) / 2 and x = (-8 - 4) / 2`
`x = (- 4) / 2 and x = (-12) / 2`
`x = - 2 and x = -6`