Question

The roots of the quadratic equation \(a^{2}p^{2}x^{2}-q^{2}=0\) are:

• A. \(\dfrac{a^{2}p^{2}}{q^{2}}\)
• B. \(\dfrac{ap}{q}\)
• C. \(\dfrac{q^{2}}{ap}\)
• D. \(\pm\,\dfrac{q}{ap}\)

Hint:

Whenever you see \(A^{2}-B^{2}=0\), factor it as \((A-B)(A+B)=0\) to get roots quickly.

Answer 1

The Correct Option is D

Step 1: Recognize the equation as a difference of squares.
\(a^{2}p^{2}x^{2}-q^{2} = (apx)^{2}-q^{2} = (apx-q)(apx+q).\)
Step 2: Set each factor equal to zero and solve for \(x\).
From \(apx-q=0 \Rightarrow x=\dfrac{q}{ap}\).
From \(apx+q=0 \Rightarrow x=-\dfrac{q}{ap}\).
Step 3: Conclude.
Hence, the roots are \(x=\pm\dfrac{q}{ap}\).