### Chapter 2: Polynomials

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.

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

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

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

x3 – (α + β + $\gamma$ )x2 + (αβ+ β$\gamma$  + $\gamma$α)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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