Question

verify that 3, -1,-1/3 r the zero of the cubic polynomial p(x)=3x cube -11×-3 then verify the relationship between zero and coefficient ​

Answer 1

Given zeroes of the cubic polynomial

p(x) = 3x3 - 11x - 3

Here

a = 3

b = -11

c = -3

alpha = 3

beta = -1

gama = -1/3

1) Sum of three zeroes

=> alpha + beta + gama = -b/a

2) Sum of the product of 2 zeroes

=> alpha.beta +beta.gama + gama.alpha

= c/a

3) Product of three zeroes

=> alpha × beta × gama = -d/a

4) X3 - ( alpha + beta + gama ) X2 + ( alpha.beta+beta.gama+gama.alpha )X - alpha × beta × gama