The sum and product of the roots of a quadratic equation are \(\frac{4}{7}\) and \(\frac{5}{7}\) respectively. Find its equation.
A. \(7x^{2} - 4x - 5 = 0\) B. \(7x^{2} - 4x + 5 = 0\) C. \(7x^{2} + 4x - 5 = 0\) D. \(7x^{2} + 4x + 5 = 0\)
Correct Answer: B
Explanation
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: \(ax^{2} + bx + c = 0 \) = \(7x^{2} - 4x + 5 = 0\)
