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 is B

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: \(ax^{2} + bx + c = 0 \)

= \(7x^{2} - 4x + 5 = 0\)