Question

Write a quadratic polynomial, sum of whose zeros is 2√3 and their product is 2.

Answer 1

The sum of the two zeros of the quadratic equation is given by \(-b/a\)

Here it’s given \(-b/a\) = 2\(\sqrt{3}\)

The product of the quadratic equation is \(c/a\)

Here \(c/a\) = 2

the quadratic equation is of the form ax² + b x + c = 0

or x² + (sum of the roots) x + product of the roots = 0

\(=\text{x}^2-2\sqrt{3}\) x + 2

f(x) = k(x² – \(2\sqrt{3}\) x + 2), where k is any real number