Question

For what values of k, the equation 9x2+6kx+4=0 has equal roots?​

Answer 1

If equation has equal roots then,,

Discriminant (D) = 0

D = b² - 4ac = 0

==: 9x² + 6kx + 4 = 0

a = 9 , b = 6k , c = 4

D = 36k² - 144 = 0

(6k)² - (12)² = 0

(6k - 12) (6k + 12) = 0

k = 2

Answer 2

Answer:

Since, 9x

2

+6kx+4=0 has equal roots.

Then, b

2

−4ac⩾0

(6k)

2

−4(9)(4)⩾0

36k

2

−36(4)⩾0

36(k

2

−4)=0

k

2

−4=0

k

2

=2

2

k=±2

Let us check

9x

2

+6(2)x+4=0

9x

2

+12x+4=0

9x

2

+6x+6x+4=0

3x(3x+2)+2(3x+2)=0

(3x+2)(3x+2)=0

∴x=

3

−2

,

3

−2