Question

If $a x^2+b x+c=0$ with real coefficients $a, b, c$ and $a \neq 0$, then
I. Discriminant, $D=b^2-4 a c$.
II. For $D \geq 0$, equation has real roots.
III. For $D< 0$, equation has imaginary roots.
IV. For $D< 0, x=\frac{-b \pm i \sqrt{4 a c-b^2}}{2 a}$.

• A. I and II are correct
• B. II, III and IV are correct
• C. I, II and IV are correct
• D. All are correct

Answer 1

Answer: (D)

If $a x^2+b x+c=0$ is the quadratic equation, $a, b$ and $c \in R, a \neq 0$.
Then, discriminant, $D=b^2-4 a c$
By quadratic formula,
$x=\frac{-b \pm \sqrt{D}}{2 a}$
$\therefore$ Root of quadratic equation will be positive, if $D \geq 0$ and roots of quadratic equation will be negative, if $D< 0$
$ x=\frac{-b \pm \sqrt{\left(b^2-4 a c\right)}}{2 a}$
$ x=\frac{-b \pm i \sqrt{4 a c-b^2}}{2 a}$