Question

Form a quadratic equation whose one root is 2+√5 and sum of the roots is 4

Answer 1

To form a quadratic equation, let α and β be the two roots.

Let us assume that the required equation be ax² + bx + c = 0 (a ≠ 0).

According to the problem, roots of this equation are α and β.

Therefore,

α + β = - ba and αβ = ca.

Now, ax2 + bx + c = 0

⇒ x2 + bax + ca = 0 (Since, a ≠ 0)