Question

A quadratic equation with rational coefficients has both roots real and irrational, if the discriminant is

• A. a perfect square
• B. positive, but not a perfect square
• C. negative, but not a perfect square
• D. zero

Answer 1

Answer: (B)

positive, but not a perfect square

The two roots of a quadratic equation are given by
$\frac{-b+\sqrt{b^2-4ac}}{2a}and\frac{-b-\sqrt{b^2-4ac}}{2a}$
where $\sqrt{b^2-4ac}$ is the discriminant.
If the discriminant is positive but no t a perfect square, then
$\sqrt{b^2-4ac}$ is irrational
In this case the equation will have both roots real and irrational.
If the discriminant is negative then the roots are complex.
Hence, the correct option is B.