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 quadratic equation be \(ax^2 + bx + c = 0\). According to the problem, we have: Sum of the roots: \(-\frac{b}{a} = \frac{4}{7}\) Product of the roots: \(\frac{c}{a} = \frac{5}{7}\) Using the formula for the sum and product of roots, we get: \(-\frac{b}{a} = \frac{4}{7} \implies b = -\frac{4}{7}a\) \(\frac{c}{a} = \frac{5}{7} \implies c = \frac{5}{7}a\) Substituting these values in the quadratic equation, we get: \(ax^2 - \frac{4}{7}ax + \frac{5}{7}a = 0\) Multiplying both sides by \(\frac{7}{a}\), we get: \(7x^2 - 4x + 5 = 0\) Therefore, the quadratic equation is \(7x^2 - 4x + 5 = 0\).