Question

Verify that 3, -1,-1/3are the zeroes of the cubic polynomial
p(x) = 3x³ – 5x²- 11x - 3, and then verify the relationship between the zeroes and the
coefficients.​

Answer 1

Step-by-step explanation:

p(x)=3x^3-5x^2-11x-3

so,

let x+1=0

x=-1

p(-1)=(-3)-5+11-3

=-11+11

=0

so, (x+1) is one of the zero of polynomial

next

x-3=0

x=3

p(3)=81-45-33-3

= 81-81

=0

so, (x-3) is a zero

next

x+1/3=0

x=-1/3

p(-1/3)=(-1/9)-5/9+11/3-3

=-33/9+33/9

=0

so,(x+1/3) is a zero

relationship between the zeroes and the coefficient is

alpha+beta+gama =-b/3

(-1)+3-1/3=-5/3

-5/3=-5/3