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
\(\frac{49}{36}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
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 \(\frac{3}{1}\)
= \(\frac{49}{12}\)
Source: Myschool Past Questions Archive (Record #32227)