Question

solution of 9x²+3kx+4=0​

Answer 1

Given quadratic equation is= 9x² + 3kx + 4 = 0

On comparing with standard form of quadratic equation i.e ax² + bx + c =0,a≠0

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

D(discriminant)= b²-4ac

= (3k)² - 4× 9 ×4

= 9k² - 144

Since, roots of given equation are distinct.  D > 0.

9k² - 144 > 0

9(k² - 16) >0

(k² - 16) >0            (9≠0)

k² -4²>0

(k-4) (k+4) >0

[ a² - b² = (a-b)(a+b)]

k > 4 and k< -4

Hence, the value of k is k > 4 and k< -4.

HOPE THIS WILL HELP YOU..

Answer 2

The given quadratic equation is :

9x2 + 3kx + 4 = 0

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

This equation has real roots if

b2 - 4ac ≥ 0

⇒ (3k)2 - 4 x 9 x 4 ≥ 0

⇒ 9k2 - 144 ≥ 0

⇒ 9k2 ≥ 144

⇒ k2 ≥ 144/9

⇒ k ≥ 12/3

⇒ k ≥ 4.

hope this helped u