Find the equation whose roots are -2/3 and -1/4
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Correct Answer: Option A
Explanation:
x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)
x = \(-\frac{2}{3}\) and \(-\frac{1}{4}\)
\(\implies (x + \frac{2}{3}) = 0; (x + \frac{1}{4}) = 0\)
\((x + \frac{2}{3})(x + \frac{1}{4}) = 0\)
\(x^{2} + \frac{1}{4}x + \frac{2}{3}x + \frac{1}{6} = 0\)
\(x^2 + \frac{11}{12}x + \frac{1}{6} = 0\)
\(12x^2 + 11x + 2 = 0\)