Q5 of 31 Page 1

If 2 is a root of the equation x2 + kx + 12 = 0 and the equation x2 + kx + q = 0 has equal roots, find the value of q.

2 is a root of the equation, x2 + kx + 12 = 0.


Therefore, 2 must satisfy the equation


⇒ 22 + k(2) + 12 = 0


⇒ 4 + 2k + 12 = 0


⇒ k = –8


Now, x2 + kx + q = 0 has equal roots.


Concept used:


If a quadratic equation ax2 + bx + c = 0 has equal root, then


D = b2 – 4ac = 0


Now, for second equation


a = 1


b = k = –8


c = q


D = b2 – 4ac


⇒ 0 = (–8)2 – 4(1)(q)


⇒ 64 = –4q


⇒ q = 16


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