Question

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

Answer 1

Here is your answer....

2x^2 + px - 15 = 0

since -5 is the root of above equation...so put x = -5

2 × (-5)^2 + p(-5) - 15 = 0

2 × 25 - 5p -15 = 0

50 - 15 = 5p

so, p = 7

put value of p in another equation....

7 (x^2 + x ) + k = 0

7x^2 + 7x + k = 0

since it has equal roots...

therefore b^2 - 4ac = 0

here a = 7 , b= 7 and c = k

place the values of a , b and c

7^2 - 4 × 7 × k = 0

49 - 28k = 0

so, k = 49/28

hope this will help you...

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