Which of the following quadratic equations has \(-\frac{1}{2}\) and \(\frac{3}{4}\) as its roots?

  • A 8x2 + 11x - 3 = 0
  • B 8x2 -11x – 3 = 0
  • C 8x2 + 2x -3 = 0
  • D 8x2 - 2x – 3 = 0
waec 2004mathematics

The correct answer is D. 8x2 - 2x – 3 = 0

X2 - (sum of the roots)x + (product of the roots) = 0

Sum of the roots \(= -\frac{1}{2}+\frac{3}{4} = \frac{-2+3}{2}=\frac{1}{4}\)

Product of the roots = \(-\frac{1}{2}\times \frac{3}{4}=\frac{-3}{8}\\

X^2-\left(\frac{1}{4}\right)x-\frac{3}{8} = 0. Taking \hspace{1mm}the\hspace{1mm} common\)

\(8x^2-2x-3=0\);

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