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, find the value of k.
Given that – 5 is a root of the quadratic equation 2x2 + px – 15 = 0
2(– 5)2 – 5p – 15 = 0
5p = 35
p = 7
Given equation is p (x2 + x) + k = 0
px2 + px + k = 0
Comparing with standard quadratic equation ax2 + bx + c = 0
a = p b = p c = k
Given that the roots of equation are equal
Thus D = 0
Discriminant D = b2 – 4ac = 0
[p]2 – 4.p.k = 0
72 – 28k = 0
49 – 28k = 0
The value of k is 
for which roots of the quadratic equation are equal.
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