x^3 – 4x^2 + 5x – 2;2, 1, 1

Question

Verify that the numbers given alongside of the cubic polynomial are their zeros. Also verify the relationship between the zeroes and the coefficients in each case :

x³ – 4x² + 5x – 2;2, 1, 1

Answer 1

Let p(x) = x³ – 4x² + 5x – 2

Then, p(2) = (2)³ – 4(2)² + 5(2) – 2

= 8 – 16 + 10 – 2

= 0

p(1) = (1)³ – 4(1)² + 5(1) – 2

= 1 – 4 + 5 – 2

= 0

Hence, 2, 1 and 1 are the zeroes of the given polynomial x³ – 4x² + 5x – 2.

Now, Let α = 2 , β = 1 and γ = 1

Then, α + β + γ = 2 + 1 + 1 = 4

αβ + βγ + γα = (2)(1) + (1)(1) + (1)(2)

= 2 + 1 + 2

= 5

and αβγ = 2 × 1 × 1

= 2

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