Chapter 2: Polynomials

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Q
Polynomials CBSE NCERT Solutions

Question:

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.

Answer:

Solution: Suppose that α, β and \gamma  be the roots of the cubic polynomial.
We have,

(α + β + \gamma ) = 4, (αβ+ β\gamma  + \gammaα) = 1 and (αβ\gamma ) = – 6
We know,

The cubic polynomial with roots α, β, and \gamma  is:

x3 – (α + β + \gamma )x2 + (αβ+ β\gamma  + \gammaα)x – (αβ\gamma
= x3 – (4)x2 + (1)x – (– 6)
= x3 – 4x2 + x + 6 , which is the required cubic polynomial.

Hence, the cubic polynomial is x3 – 4x2 + x + 6. 

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