Question

Use the discriminant to describe the roots of each equation. Then select the best description. x2 + 9x + 14 = 0 double root real and rational root real and irrational root imaginary root

Answer 1

General quadratic equation is given by

$ax^2+bx+c=0$

compare given equation $x^2+9x+14=0$

with that equation, we get:

a=1, b=9, c=14

Now discriminant is given by formula

$D=b^2-4ac$

Plug above values to find discriminant

$D=9^2-4(1)(14)$

$D=81-56$

$D=25$

Hence discriminant is 25

When discriminant is a positive non zero number then that indicates two different real roots which can be rational too.

Hence final answer is "real and rational root ".