Q5 of 47 Page 1

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

Let f(x) = 2x2 + px - 15


As - 5 is a root of f(x)


f(- 5) = 0


2(- 5)2 + p(- 5) - 15 = 0


2(25) - 5p - 15 = 0


50 - 15 = 5p


5p = 35


p = 7 [eqn 1]


So the quadratic eqn


p(x2 + x) + k = 0 is


7(x2 + x) + k = 0


7x2 + 7x + k = 0


Any quadratic equation will have real roots if


b2 - 4ac = 0 [ for any quadratic eqn ax2 + bx + c]


72 - 4(7)(k) = 0


49 - 28k = 0



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