Question

For the quadratic equation $a{x}^2+bx+c=0,a,b,c,\in Q$, If $D=0$ then ...................
Choose the correct option in respect to the statements below.
(P) The roots of the equation are equal.
(Q) The roots of the equation are not equal.
(R) The roots of the equation are rational numbers.
(S) The roots of the equation has no roots.

• A. Statements $P$ and $R$ are correct
• B. Statements $Q$ and $R$ are correct
• C. Only statement $S$ is correct
• D. Only statement $P$ is correct

Answer 1

The correct option is A Statements $P$ and $R$ are correct

For the quadratic equation $a{x}^2+bx+c=0,a,b,c,\epsilon Q$

Roots are given by

$\alpha =\frac{-b+\sqrt{b^2-4ac}}{2a}$ and

$\beta =\frac{-b-\sqrt{b^2-4ac}}{2a}$

If $D=0$ then $\alpha =\frac{-b}{2a}=\beta$ i.e. the roots are equal and real.

Since $a,b$ and $c\in Q$, the roots will be equal and rational.

Hence, statements P and R are correct.