Question

What will be the polynomial if the value of α + β + γ = -√3 , αβ + βγ + γα = 4 and = \(\frac {-5}{3}\)?

(a) x^3 + 3x^2 + 12x + 5

(b) 3x^3 + √3 x^2 + 4x + 5

(c) 3x^3 + 3√3 x^2 + 12x + 5

(d) x^3 + √3 x^2 + 12x + 5

I got this question in unit test.

Origin of the question is Zeros and Coefficients of Polynomial topic in section Polynomials of Mathematics – Class 10

Answer 1

Correct answer is (c) 3x^3 + 3√3 x^2 + 12x + 5

Explanation: α + β + γ = – √3, + βγ + γα = 4, αβγ = \(\frac {-5}{3}\)

∴ f(x) = x^3 – (α + β + γ) x^2 + (αβ + βγ + γα)x – αβγ

Substituting we get,

f(x) = x^3 + √3 x^2 + 4x + \(\frac {5}{3}\)

f(x) = 3x^3 + 3√3 x^2 + 12x + 5