Question

If - 5 is root of quadratic equation 2xsquare +px-15=0 and quadratic equation p(x square +x) +k=0 has equal roots then 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