NCERT Solutions for Class 10 Maths Chapter 2

Important NCERT Questions

Polynomials

NCERT Books for Session 2022-2023

CBSE Board and UP Board Others state Board

EXERCISE 2.4

Page No:36

Questions No:2

# Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively.

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Let, p(x) = ax³ + bx² + cx + d be a cubic polynomial whose zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.

Given that,

α + β + γ = 2

αβ + βγ + γα = -7

αβγ = -14

We know that,

α + β + γ = -(Cofficient of x²)/(Cofficient of x³)

αβ + βγ + γα = (Cofficient of x)/(Cofficient of x³)

αβγ = -(Constant term)/Cofficient of x³)

Therefore,

α + β + γ = -(Cofficient of x²)/(Cofficient of x³) = (-b)/a = 2/1

αβ + βγ + γα = (Cofficient of x)/(Cofficient of x³) = c/a = (-7)/1

αβγ = -(Constant term)/Cofficient of x³) = (-d)/a = (-14)/1

On comparing, a = 1, b = -2, c = -7 and d = 14

Hence, the required cubic polynomial is p(x) = x³ – 2x² – 7x + 14.

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