Question

If \(\alpha,\beta,\gamma\) are zeroes of the cubic polynomial \(ax^{3}+bx^{2}+cx+d=0\), then the value of \(\alpha\beta\gamma\) is

• A. \(\dfrac{b}{a}\)
• B. \(-\dfrac{c}{a}\)
• C. \(-\dfrac{d}{a}\)
• D. \(\dfrac{c}{a}\)

Hint:

Signs in Vieta alternate: for cubic, product of roots is \(-d/a\).

Answer 1

The Correct Option is C

Step 1: Use Vieta’s relation for cubics.
For \(ax^{3}+bx^{2}+cx+d\): \(\alpha\beta\gamma=-\dfrac{d}{a}\).
Step 2: State result.
Hence \(\alpha\beta\gamma=-\dfrac{d}{a}\).