Question

for what value of k, the equation 9x^2+6kx+4=0 has equal roots?​

Answer 1

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= --2/3 ; −2/3