Question 8
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is −1, then the product of the other two zeroes is:
b – a + 1 (b) b – a – 1
(c) a – b + 1 (d) a – b − 1
Let p(x) = x3 + ax2 + bx + c
Given that one zero is −1
∴ 𝜶 = −1,
and we need to find product of other other two zeroes, i.e. 𝜷𝜸
We know that
Product of Zeroes = (−𝐷)/𝐴
𝜶𝜷𝜸 = (−𝑐)/1
−1 × 𝛽𝛾 = −c
𝜷𝜸 = c
Now, we need to c in terms a and b
Since −1 is a zero of p(x)
p(−1) = 0
Putting x = −1
(−1)3 + a(−1)2 + b(−1) + c = 0
−1 + a − b + c = 0
c = b − a + 1
From (1): Putting 𝜷𝜸 = c
𝜷𝜸 = b − a + 1
So, the correct answer is (A)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.