Verify that 1,2,3 are the zeroes of the cubic polynomial
p(x)`=x^(3)-6x^(2)+11x-6` and verify the relation between its zeroes and coefficients.

Answer

N/a

Explanation

Here, `" " p(x)=x^(3)=6x^(2)+11x-6`
`implies " " p(1)=1^(2)-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`
and `" " p(3)=3^(3)-6(3)^(2)+11(3)-6=27-54+33-6=0`
`:.` 1,2 and 3 are zeroes of p(x).
Now, `" " alpha+beta+gamma=1+2+3=6-(-6)/(1)=-("coefficient of" x^(2))/("coefficient of" x^(3))`
`alphabeta+beta+alpha gamma=(1)(2)+(2)(3)+(3)(1)=+6+3=11`
`=(11)/(1)=("coefficient of" x)/("coefficient of "x^(3))` Hence Verified.