Find the equation whose roots are -2/3 and -1/4
A
12x2 + 11x + 2 = 0
B
12x2 - 11x + 2 = 0
C
x2 - 11/12x + 2 = 0
D
12x2 - 11x - 2 = 0
E
x2 - 11/12x - 2 = 0
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
Source: Myschool Past Questions Archive (Record #22874)