Question

Find the discrimanant and the number of real roots for this equation 9x^2+12x+4=0

Answer 1

For this case we have that by definition, the discriminant of a quadratic equation $ax ^ 2 + bx + c = 0$, is given by:

$d = b ^ 2-4 (a) (c)$

$d> 0$: Two different real roots

$d = 0$: Two equal real roots

$d$: Two different complex roots

If we have $9x ^ 2 + 12x + 4 = 0$, then:

$a = 9\\b = 12\\c = 4$

Substituting the values:

$d = 12 ^ 2-4 (9) (4)\\d = 144-144\\d = 0$

Thus, we have two equal real roots.

ANswer:

We have two equal real roots.