Question

If the roots of the equation $a{x}^2+bx+c=0$ are real and distinct, then

• A. both roots are greater than $\frac{-b}{2a}$
• B. both roots are less than $\frac{-b}{2a}$
• C. one of the roots exceeds $\frac{-b}{2a}$
• D. None of these

Answer 1

Answer: (C)

one of the roots exceeds $\frac{-b}{2a}$

Given equation : $a{x}^2+bx+c=0$

It is given that the roots of the equation

are real and distinct, i.e. Discriminant > 0

$\Rightarrow b^2-4ac>0$

Now, applying Shri Dharacharya formula to

solve the equation we get.

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

As, we can see that ,

$\frac{-b-\sqrt{b^2-4ac}}{2a}<\frac{-b}{2a}<\frac{-b+\sqrt{b^2-4ac}}{2a}$

$(\because b^2-4ac>0)$

$\therefore$ One of the roots of the given equation exceeds $\frac{-b}{2a}$