Multiple choice

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

  1. 49 4

  2. 4 49

  3. 4

  4. None of these
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A Correct answer
Explanation

Substituting x = 4 gives 16 + 4p + 12 = 0, so p = -7. Equal roots require p^2 - 4q = 0, giving q = 49/4, which is the intended value of option A.

AI explanation

Substitute x = 4 into the first equation x^2 + px + 12 = 0 to find p, giving 16 + 4p + 12 = 0. Solving this yields 4p = -28, so p = -7. Substitute p = -7 into the second equation x^2 - 7x + q = 0. Since this equation has equal roots, its discriminant must equal zero, so (-7)^2 - 4(1)(q) = 0. Solving 49 - 4q = 0 gives q = 49/4.

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