Multiple choice

If -4 is a root of the quadratic equation x2 + px - 4 = 0 and the quadratic equation x2 + px + k = 0 has equal roots, find the value of k.

  1. 3 4

  2. 7 2

  3. 2 9

  4. 9 4
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D Correct answer
Explanation

Substituting x = -4 gives 16 - 4p - 4 = 0, so p = 3. Equal roots require 3^2 - 4k = 0, hence k = 9/4.

AI explanation

Substitute the root -4 into x^2 + px - 4 = 0 to get (-4)^2 + p(-4) - 4 = 0, which simplifies to 16 - 4p - 4 = 0, giving p = 3. Now substitute p = 3 into the second equation to get x^2 + 3x + k = 0. Since this equation has equal roots, its discriminant (b^2 - 4ac) must equal zero, so 3^2 - 4(1)(k) = 0, which simplifies to 9 - 4k = 0 and yields k = 9/4. The value of k is 9/4.

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