Question

What we can say about the nature of roots of $x^2–2x–3=0$ ?

• A. Both the roots are natural numbers
• B. Both the roots are integers
• C. One of the root is zero
• D. Roots are not real

Answer 1

The correct option is B

Both the roots are integers

Given equation $x^2–2x–3=0$

Nature of roots for$a{x}^2+bx+c=0\text{is}\Delta =b^2-4ac\Delta =(-2{)}^2–4(-3\left)\right(1)=4+12=16$.

$\Delta$ is a perfect square
$\therefore$ The roots are rational and unequal.
$\left(or\right)$

Solving the equation,
$x=\frac{-(-2)\pm \sqrt{16}}{2\times 1}=\frac{2\pm 4}{2}x=\frac{2+4}{2},\frac{2-4}{2}x=3,-1$
Thus, both the roots are integers.