Question

The equation 12x² + 4kx + 3 = 0 has real and equal roots, find value of k.

Answer 1

The given quadratic equation is 12x² + 4kx + 3 = 0, comparing it with ax² + bx + c = 0.

⇒  We get, a = 12,b = 4k and c = 3

⇒  It is given that roots are real and equal.

∴  b²−4ac = 0

⇒  (4k)²−4(12)(3)=0

⇒  16k²−144 = 0

⇒  16k² = 144

⇒  k²= 144/16​

⇒  k² = 9

∴   k = ±3