Question

For $a,b\in R^{+},$ match the following quadratic equations with their corresponding roots.

• A. $x=\frac{-1\pm \sqrt{1-4ab}}{2a}$
• B. $x=0;\frac{-b}{a}$
• C. No Real Roots
• D. $x=\frac{-b\pm \sqrt{b^2-4a}}{2}$

Answer 1

$\left(i\right)a{x}^2+bx=0$
$\Rightarrow x(ax+b)=0$
$\Rightarrow x=0$ or $x=\frac{-b}{a}$

$\left(ii\right)x^2+bx+a=0$
Using quadratic formula,
$\Rightarrow x=\frac{-b\pm \sqrt{b^2-4a}}{2}$

$\left(iii\right)a{x}^2+b=0$
$\Rightarrow a{x}^2=-b$
$\Rightarrow x^2=\frac{-b}{a}$
$\Rightarrow x=\pm \sqrt{\frac{-b}{a}}$
Since, $a,b\in R^{+}\Rightarrow \frac{-b}{a}<0$
Thus, no Real Roots

$\left(iv\right)a{x}^2+x+b=0$
Using quadratic formula,
$\Rightarrow x=\frac{-1\pm \sqrt{1-4ab}}{2a}$