Question

With respect to the roots of $x^2–2x–3=0$, we can say that the roots are .

• A. real and equal
• B. real and distinct
• C. imaginary

Answer 1

The correct option is B real and distinct

Step 1:- For $x^2–2x–3=0$, value of discriminant
$D=(-2{)}^2–4(-3\left)\right(1)=4+12=16$.

Step 2:- Since, D is a perfect square, roots are rational and unequal.

Step 3:- Solving the equation,
$x=\frac{-(-2)+\sqrt{(}16)}{2}or\frac{-(-2)-\sqrt{(}16)}{2}$
$x=3,-1$
Thus, the roots are real and distinct.