Question

# Question 5 Given that one of the zeroes of the cubic polynomial ax3+bx2+cx+d is zero, the product of the other two zeroes is (a)−ca (b)ca (c)0 (d)−ba

Solution

## Let α,β and γ are the zeros of  p(x)=ax3+bx2+cx+d Given that, one of the zeroes of the cubic polynomial p(x) is zero (α=0). We know that, Sum of product of zeroes taken two at a time = ca ⇒ αβ+βγ+γα=ca ⇒ 0×βγ+γ×0=ca  ⇒ 0+βγ+0=ca ⇒ βγ=ca Hence, product of other two zeroes = ca So option B is correct. Mathematics

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