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For the cubic polynomial $p(x)=2x^3-5x^2-14x+8$, what is the sum of the products of its zeroes taken two at a time?
A$-7$
B$7$
C$-\dfrac{7}{2}$
D$\dfrac{7}{2}$
Answer & Solution
Correct answer: A. $-7$
For a cubic polynomial $ax^3+bx^2+cx+d$, if the zeroes are $\alpha,\beta,\gamma$, then $\alpha\beta+\beta\gamma+\gamma\alpha=\dfrac{c}{a}$. Here $a=2$ and $c=-14$, so the value is $\dfrac{-14}{2}=-7$.
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