Question

If \(\alpha,\beta\) are the roots of \(ax^2+bx+c=0\), then \[ \left(\frac{\alpha}{\beta}-\frac{\beta}{\alpha}\right)^2 = \]

• A. \(\dfrac{b^2(b^2-4ac)}{a^2c^2}\)
• B. \(\dfrac{b^2(b^2-4ac)}{a^4}\)
• C. \(\dfrac{b^2(b^2-4ac)}{ca^3}\)
• D. \(\dfrac{b^2(b^2-4ac)}{c^4}\)

Hint:

Useful relations: \[ \boxed{ \alpha+\beta=-\frac{b}{a},\qquad \alpha\beta=\frac{c}{a} } \]

Answer 1

The Correct Option is A