Question

$a{x}^2+bx+c=0$ is quadratic equations with real coefficients $a$ , $b$ and $c$.which of the following statement is/are not true ?

• A. If $a=b=c=0$ then may be no roots are possible.
• B. If $a=b=c=0$ then it must have infinite number of roots.
• C. if $a$ , $b$ and $c$ are rational then then irrational roots must be in conjugate pairs.
• D. if $a$ , $b$ and $c$ are irrational then irrational roots may be in conjugate pairs.

Answer 1

The correct option is A If $a=b=c=0$ then may be no roots are possible.

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

The roots of given equation are $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

If $a=b=c=0$ , then any value for $x$ will satisfy the equation

So there will be infinite roots

Therefore If $a=b=c=0$ then may be no roots are possible is wrong statement

So option $A$ is correct