If the equation 9x^2 + 6kx + 4 = o has equal roots, then the roots are both equal to ? A. ±3/2 B. ±3/2 c. 0 D. ±

Question

If the equation 9x² + 6kx + 4 = o has equal roots, then the roots are both equal to ?

A. \(\pm\frac{3}{2}\)

B. \(\pm\frac{3}{2}\)

C. 0 

D. ± 3

Answer 1

Given: the equation 9x² + 6kx + 4 = o has equal roots.

To find: the roots are both equal to ? 

Solution: If roots of given equation are equal then D = b² – 4ac = 0

⇒ (6k)² – 4(9)(4) = 0 

⇒ 36k² – 144 = 0 

⇒ 36k² = 144 

⇒ K² = 4

⇒ K = \(\pm2\)

Case 1 :- when k = 2 

In equation 9x² + 6 k x + 4 = 0 

9x² + 6(2) x + 4 = 0 

9x² + 12 x + 4 = 0 

(3x)2 + 2 × 2 × 3x + (2)² = 0 

(3x + 2)² = 0 

3 x + 2 = 0 

3x = – 2

\(x=-\frac{2}{3}\)

Case 2 :- when k = – 2

In equation 9x² + 6kx + 4 = 0

9x² + 6(– 2) x + 4 = 0

9x² – 12 x + 4 = 0

(3x)² – 2 X 2 X 3x + (2)² = 0

(3x – 2)² = 0

3x – 2 = 0

3x = 2

\(x=\frac{2}{3}\) So the roots of the given quadratic equation are \(\pm\frac{2}{3}\)