\frac{7}{36}
- \frac{36}{7}
\frac{36}{7}
- \frac{7}{36}
Correct answer is D
The general form of a quadratic equation is:
x^2 -(sum of roots)x +(product of roots) = 0
7x^2+12x-4=0
Divide through by 7
=x^2+\frac{12}{7}x-\frac{4}{7}=0
=x^2-(-\frac{12}{7})x+(-\frac{4}{7})=0
\therefore sum of roots = -\frac{12}{7}, and products of roots =-\frac{4}{7}
α + β = -\frac{12}{7}, αβ = -\frac{4}{7}
\frac{αβ}{(α + β)^2} = \frac{\frac{-4}{7}}{(\frac{-12}{7})^2}
=\frac{\frac{-4}{7}}{\frac{144}{49}}=-\frac{4}{7}\times\frac{49}{144}
\therefore - \frac{7}{36}
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