Question 8 - MCQs from NCERT Exemplar - Chapter 2 Class 10 Polynomials

Last updated at April 16, 2024 by Teachoo

If one of the zeroes of the cubic polynomial x
^{
3
}
+ ax
^{
2
}
+ bx + c is −1, then the product of the other two zeroes is:

(a)b – a + 1 (b) b – a – 1

(c) a – b + 1 (d) a – b − 1

Transcript

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
So, the correct answer is (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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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