Question

If $a{x}^2+bx+c=0$ has two distinct real roots and $a{x}^2+b|x|+c=0$ has three distinct real roots, then

• A. c > 0
• B. c < 0
• C. “c” can be any real number
• D. c = 0

Answer 1

The correct option is D c = 0

Case (i):- suppose $x\ge 0$
Given equation is $a{x}^2+bx+c=0$
roots are $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
ii):- sup x < 0
Given equation is $a{x}^2-bx+c=0$
roots are $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
If c =0, Then $a{x}^2+b|x|+c=0$ has three distinct real roots.