Question

if x=-2 is a root of the equation 3x^2+7x+p=0 and the equation x^2+k(4x+k-1)+p=0 has equal roots then find the value of k

Answer 1

I hope it's helpful.

Answer 2

Here, x = – 2 is the root of the equation

3x^2 + 7x + p = 0

⇒ 3(– 2)2 + 7(– 2) + p = 0

⇒ p = 2

Root of the equation x^2 + 4kx + k^2 – k + 2 = 0  are equal.

⇒ b^2 – 4ac = 0

⇒ 16k^2 – 4(k^2 – k + 2) = 0

⇒ 3k^2 + k – 2 = 0

⇒ (3k – 2)(k + 1) = 0

⇒ k =  2  ÷ 3  , − 1