Question

If-5 is a root of the quadratic equation 2x2+px−15=0 and the quadratic equation p(x2+x)+k=0 has equal roots, find the value of k

Answer 1

Given that (−5) is the root of 2x² + px – 15 = 0
Put x = (−5) in 2x² + px – 15 = 0
⇒ 2(−5)² + p(−5) − 15 = 0
⇒ 50 −5p − 15 = 0
⇒ 35 − 5p = 0
⇒ 5p = 35
∴ p = 7
Hence the quadratic equation p(x² + x) + k = 0 becomes, 7(x² + x) + k = 0
⇒ 7 x² + 7x + k = 0
Here a = 7, b = 7 and c = k
Given that this quadratic equation has equal roots
∴ b² – 4ac = 0
⇒ 7² – 4(7)(k) = 0
⇒ 49 – 28k = 0
⇒ 49 = 28k
∴ k = (49/28) = 7/4