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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