Question

-5 is one of the zeroes of 2x²+px-15, zeroes of p(x²+x)+k are equal to each other. 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


 

Answer 2

Answer:

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