Question

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

please answer this question​ fast ..........

Answer 1

Step-by-step explanation:

ANSWER

One of the root of the quadratic equation 2x

2

+px−15=0 is −5.

So, substitute the value x=−5 in the above equation,

2(−5)

2

+p(−5)−15=0

50−5p−15=0

35=5p

p=7

We know that the quadratic equation has equal roots when the discriminant is equal to zero.

So, p(x

2

+x)+k=0---- (1)

Put the value of p in equation 1,

7x

2

+7x+k=0

D=b

2

−4ac=0

a=7,b=7,c=k

7

2

−4×7×k=0

49=28k

k=1.75

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