The sum and product of the roots of a quadratic equation are \(\frac{4}{7}\) and \(\frac{5}{7}\) respectively. Find its equation.
Let the roots of the equation be \(\alpha\) and \(\beta\).
\(\alpha + \beta = \frac{-b}{a} = \frac{4}{7}\)
\(\alpha \beta = \frac{c}{a} = \frac{5}{7}\)
\(\implies a = 7, b = -4, c = 5\)
Equation: \(ax^{2} + bx + c = 0 \)
= \(7x^{2} - 4x + 5 = 0\)
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