Home › UP Board Class 10 › Mathematics › If $\alpha,\beta,\gamma$ are the zeroes of the c…
If $\alpha,\beta,\gamma$ are the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$, then $\alpha\beta\gamma$ is equal to
A$\dfrac{d}{a}$
B$-\dfrac{b}{a}$
C$\dfrac{c}{a}$
D$-\dfrac{d}{a}$
Answer & Solution
Correct answer: D. $-\dfrac{d}{a}$
For a cubic polynomial $ax^3+bx^2+cx+d$, the relations are $\alpha+\beta+\gamma=-\dfrac{b}{a}$, $\alpha\beta+\beta\gamma+\gamma\alpha=\dfrac{c}{a}$, and $\alpha\beta\gamma=-\dfrac{d}{a}$.
Related questions
When variables and numbers appear on both sides, you must simplify:Equations needing more than one operation are described as taking more:Once a solution is found, it should be checked by substituting it back to get a statement The product of any number and its reciprocal equals:A fraction multiplying the variable is best removed by multiplying by its:Solving x divided by 4 equals 3 gives x equal to:Solving 4x equals 20 gives x equal to:Solving x minus 8 equals 5 gives x equal to: