Verifythat 3, -1 and are the zeros of the cubic polynomial-5x-11x-3 an

1.	Verifythat 3, -1 and are the zeros of the cubic polynomial-5x-11x-3 and verify the relation between its zerosand coefficients.
Answer» If α , β, γ are roots of a cubic equation ax3 + bx2 + cx + d=0, then α + β + γ = -b/a α β +β γ + γα = c/a α βγ = -d/a Given:3, - 1 and - 1/3 are zeros of polynomial 3x^3 - 5x^2 - 11x - 3 Then,Sum of zeros = - (-5)/3 = 5/3Verify = 3 - 1 - 1/3 = (9 - 3 - 1)/3 = (9-4)/3 = 5/3 Product of pair of zeros = - 11/3Verify = 3-1 + - 1-1/3 + 3-1/3 = - 3 + 1/3 - 1 = - 4 + 1/3 = (-12 + 1)/3 = - 11/3 Product of zeros = - (- 3)/3 = 1Verify = 3-1*-1/3 = 3/3 = 1

Verifythat 3, -1 and are the zeros of the cubic polynomial-5x-11x-3 and verify the relation between its zerosand coefficients.

Answer»

If α , β, γ are roots of a cubic equation ax3 + bx2 + cx + d=0, then

α + β + γ = -b/a

α β +β γ + γα = c/a

α βγ = -d/a

Given:3, - 1 and - 1/3 are zeros of polynomial 3x^3 - 5x^2 - 11x - 3

Then,Sum of zeros = - (-5)/3 = 5/3Verify = 3 - 1 - 1/3 = (9 - 3 - 1)/3 = (9-4)/3 = 5/3

Product of pair of zeros = - 11/3Verify = 3*-1 + - 1*-1/3 + 3*-1/3 = - 3 + 1/3 - 1 = - 4 + 1/3 = (-12 + 1)/3 = - 11/3

Product of zeros = - (- 3)/3 = 1Verify = 3*-1*-1/3 = 3/3 = 1