Multiple choice

If the value of a quadratic polynomial p(x) is 0 only at x = - 1 and p (- 2) = 2, then the value of p (2) is

  1. 18

  2. 9

  3. 6

  4. 3
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A Correct answer
Explanation

p(x) = k(x+1)(x-a). p(-2) = k(-1)(-2-a) = 2 => k(2+a) = 2. Since it's a quadratic with only one root at x=-1, it must be of the form p(x) = k(x+1)^2. p(-2) = k(-1)^2 = k = 2. So p(x) = 2(x+1)^2. p(2) = 2(3)^2 = 18.

AI explanation

Because the polynomial p(x) is zero only at x = -1, its form is p(x) = a(x + 1)^2. Using the given condition p(-2) = 2, we substitute to get 2 = a(-2 + 1)^2, which simplifies to a = 2. The polynomial is p(x) = 2(x + 1)^2, so evaluating p(2) gives 2(2 + 1)^2. This yields 2 * 9, making the final result 18.

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