Question

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

Answer 1

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

p(3) = 3(3)³ – 5(3)² – 11(3) – 3

= 81 – 45 – 33 – 3

= 0

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

So, we take α = 3, β = – 1, γ = -1/3

Verification

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