Multiple choice

If $x = 2$ and $x = 3$ are zeros of the quadratic polynomial $x^2 + ax + b$, the values of $a$ and $b$ respectively are

  1. $5,- 6$
  2. $- 5, - 6$
  3. $-5, 6$
  4. $5, 5$
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C Correct answer
Explanation

If 2 and 3 are zeros, the polynomial is (x-2)(x-3) = x^2 - 5x + 6. Comparing to x^2 + ax + b, a = -5 and b = 6.

AI explanation

If x = 2 and x = 3 are the zeros of the polynomial, then the polynomial can be expressed as (x - 2)(x - 3) = 0 based on the factor theorem. Expanding this product using FOIL yields x^2 - 3x - 2x + 6 = 0. Combining the x terms simplifies the polynomial to x^2 - 5x + 6 = 0. By matching the coefficients with the standard form x^2 + ax + b, we find that a = -5 and b = 6.

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