Question

If -5 is a root of the quadratic equation 2x² + px - 15 = 0 and the quadratic equation p(x²+x) + k = has equal roots, find the value of k
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Answer 1

Answer:

Since −5 is a root of the equation 2x

2

+px−15=0. Therefore,

2(−5)

2

−5p−15=0⇒p=7

Putting p=7 in p(x

2

+x)+k=0 we get

7x

2

+7x+k=0

Here ,a=7,b=7;c=k

This equation will have equal roots, if

Discriminant =b

2

−4ac=0 ⇒49−4×7×k=0⇒k=

28

49

⇒k=

4

7

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