Question

The roots of $a^2{x}^2+abx=b^2,a\ne 0,b\ne 0$ are:

• A. Equal
• B. Non- real
• C. Unequal
• D. None of these

Answer 1

Answer: (C)

Unequal

Here, $a^2{x}^2+abx=b^2,a\ne 0,b\ne 0$
$\Rightarrow a^2{x}^2+abx-b^2=0$
Now, roots of the quadratic equation $=\frac{-ab\pm \sqrt{{\left(ab\right)}^2-4a^2(-b^2)}}{2a^2}$
$=\frac{-ab\pm \sqrt{5a^2{b}^2}}{2a^2}$
$=\frac{-ab\pm \sqrt{5}ab}{2a^2}$
$=\frac{-b\pm \sqrt{5}b}{2a}$
Thus, the roots are real and unequal.