If -5 is a root of the quadratic equation 2x²+px-15 . . .

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

Doubt by Mehak

Solution :

2x²+px-15=0

-5 is the root of the above quadratic equation (Given)

2(-5)²+p(-5)-15=0

2(25)-5p-15=0 50-5p-15=0 35=5p 35/5=p 7=p

p=7

p(x²+x)+k=0

7(x²+x)+k=0 [∵p=7] 7x²+7x+k=0 a=7

b=7

c=k D= b²-4ac D=(7)²-4(7)(k)

0=49-28k [∵ Roots are real and equal so D=0] -49=-28k 49=28k 49/28=k 7/4=k k=7/4

Hence, the required value of k is 7/4.