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If the quadratic function 3x2 - 7x + R is a perfect square, find R

Mathematics
JAMB 1985

If the quadratic function 3x2 - 7x + R is a perfect square, find R
  • A. \(\frac{49}{24}\)
  • B. \(\frac{49}{12}\)
  • C. \(\frac{49}{13}\)
  • D. \(\frac{49}{3}\)
  • E. \(\frac{49}{36}\)
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Correct Answer: Option B
Explanation
3x2 - 7x + R. Computing the square, we have
x2 - \(\frac{7}{3}\) = -\(\frac{R}{3}\)

(\(\frac{x}{1} - \frac{7}{6}\))2 = -\(\frac{R}{3}\) + \(\frac{49}{36}\)

\(\frac{-R}{3}\) + \(\frac{49}{36}\) = 0

R = \(\frac{49}{36}\) x \(\frac{3}{1}\)

= \(\frac{49}{12}\)

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