Question

Find the value of k for which the given equation has real roots:
9x² + 3kx + 4 = 0.

Answer 1

The given quadratic equation is:

9x² + 3kx + 4 = 0

Here, a = 9, b = 3k and c = 4.

This equation has real roots if

Calculate the discriminant D of the given equation as follows:

D = b² − 4ac

⇒ (3k)² − (4 x 9 x 4)

⇒ 9k² − 144

Since the given equation has equal roots, the discriminant must be equal to zero.

D = 0

⇒ 9k² − 144 = 0

⇒ 9k² = 144
⇒ k² = ${\displaystyle \frac{144}{9}}$
⇒ k = ${\displaystyle \sqrt{\frac{144}{9}}}$
⇒ k = ± 4

Hence, the required value is k = 4 and k = −4.