x^3 – 6x^2 + 11x – 6 ;1, 2, 3

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 – 6x² + 11x – 6 ;1, 2, 3

Answer 1

Let p(x) = x³ – 6x² + 11x – 6

Then, p(1) = (1)³ – 6(1)² + 11(1) – 6

= 1 – 6 + 11 – 6

= 0

p(2) = (2)³ – 6(2)² + 11(2) – 6

= 8 – 24 + 22 – 6

= 0
p(3) = (3)³ – 6(3)² + 11(3) – 6

= 27 – 54 + 33 – 6

= 0

Hence, 1, 2 and 3 are the zeroes of the given polynomial x³ – 6x² + 11x – 6.

Now, Let α = 1 , β = 2 and γ = 3

Then, α + β + γ = 1 + 2 + 3 = 6

αβ + βγ + γα = (1)(2) + (2)(3) + (3)(1)

= 2 + 6 + 3

= 11

and αβγ = 1 × 2 × 3

= 6

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