Question

Which of the following is a polynomial with roots 4, -5 and 7?

Answer 1

Required polynomial is (x - 4)(x + 5)(x - 7) = (x - 4)(x^2 - 2x - 35) = x(x^2 - 2x - 35) - 4(x^2 - 2x - 35) = (x^3 - 2x^2 - 35x) - (4x^2 - 8x - 140) = x^3 - 2x^2 - 35x - 4x^2 + 8x + 140 = x^3 - 6x^2 - 27x + 140