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 - Mathematics

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

Solution

Let the polynomial be ax3 + bx+ cx + d and the zeroes be α, β and γ

Then, α + β + γ = (2)/1 = (-b)/a

αβ + βγ + γα = (-7)/1 = c/a

αβγ = (-14)/1 = (-d)/a

∴ a = 1, b = -2, c = -7 and d = 14

Hence, the polynomial is  x3 - 2x2  - 7x + 14

Concept: Relationship Between Zeroes and Coefficients of a Polynomial
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NCERT Class 10 Maths
Chapter 2 Polynomials
Exercise 2.4 | Q 2 | Page 36