Multiple choice

If the quadratic equation $x^2+bx+c$ are real numbers. Find $b$ and $c$ so that the given equation has two solutions $x = \dfrac{-1}4$ and $x = \dfrac 12.$

  1. $b=\dfrac{-1}{4},c=\dfrac{-1}{8}$
  2. $b=\dfrac{-1}{2},c=\dfrac{-1}{8}$
  3. $b=\dfrac{-1}{8},c=\dfrac{-1}{4}$

  4. None of these
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A Correct answer
Explanation

For roots -1/4 and 1/2, their sum is 1/4 and their product is -1/8. Since the sum of roots is -b and the product is c, b = -1/4 and c = -1/8.

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