Verify that <span

Let p(x) = 3 x³ – 5 x² – 11x – 3

Then, p( – 1) = 3( – 1)³ – 5( – 1)² – 11( – 1) – 3

= – 3 – 5 + 11 – 3

= 0

= 0

p(3) = 3(3)³ – 5(3)² – 11(3) – 3

= 81 – 45 – 33 – 3

= 0

Hence, we verified that 3, – 1 and are the zeroes of the given polynomial.

So, we take α = 3, β = – 1,

Verification

α + β + γ

αβ + βγ + γα

and αβγ

= 1

Thus, the relationship between the zeroes and the coefficients is verified.