If α and β are the roots of \(7x2 +12x - 4 = 0\),find the

Explanation

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 = \(-\frac{12}{7}, αβ = -\frac{4}{7}\)

\(\frac{αβ}{(α + β)^2} = \frac{\frac{-4}{7}}{(\frac{-12}{7})^2}\)

=\(\frac{\frac{-4}{7}}{\frac{144}{49}}=-\frac{4}{7}\times\frac{49}{144}\)

\(\therefore - \frac{7}{36}\)