If One Root Of The Equation x2 + px + 12 = 0 Is 4, While The Equation x2 +px + q = 0 Has Equal Roots, The Value Of q is

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Question

If one root of the equation x2 + px + 12 = 0 is 4, while the equation x2 +px + q = 0 has equal roots, the value of q is

Solution

Correct option is

49/4

Since 4 is a root of x2 + px + 12 = 0, we have

        16 + 4p + 12 = 0 or p = – 7.

Further, since the roots of x2 + px + q = 0 are equal, we have

        p2 – 4q = 0   or   49 – 4q = 0.

∴               q = 49/4.

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