NCERT Solution Class X Mathematics Polynomials Question 2 (Ex 2.4)

Question 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.

Answer:

Let the polynomial be ax3 + bx2 + cx + d and the zeroes be α,β, and γ.

It is given that

α + β  +  γ = 2/1 = −b/a

α β  +  βγ + αγ  = −7 /1 = c/a

α βγ = −14/1 = −d/a

If a = 1, then b = −2, c = −7, d = 14

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

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