Multiple choice

For the quadratic equation R(x) = mx2 + nx + p, which attains its minimum value at x = -1, R(6) = 0. The product of roots of the equation is

  1. 48

  2. 84

  3. -84

  4. -48
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D Correct answer
Explanation

Vertex at x = -1 means -n/(2m) = -1, so n = 2m. R(x) = mx^2 + 2mx + p. R(6) = 36m + 12m + p = 0, so p = -48m. The equation is mx^2 + 2mx - 48m = 0. Dividing by m, x^2 + 2x - 48 = 0. Product of roots = c/a = -48/1 = -48.

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