Question

Verify that 2,1,1 are zeroes of the polynomial x3-4x2+5x-2 also verify the relation between the coefficient of the zeroes

Answer 1

p(x)=x3-4x2+5x-2
fill x 2;1;1 in each case if in all case the reminder seems to be come out to be zero then they are the zeros of polynomial P of x.
the apply the following equations to verify the relationship between the coefficients of zero.
1- 1st 0 + 2nd zero + 3rd zero=-b/a (cofficents)
2-1st 0×2nd zero× 3rd zero =-d/a
3- 1st × 2nd +2nd ×3rd+3rd ×1st=c/a


hope it help you

Answer 2

Given polynomial f(x ) =  x3 - 4x2 + 5x - 2.

2,1,1 are zeroes of polynomial then

f(2) = 8 - 16 + 10 - 2 = 0

f(1) = 1 - 4 + 5 - 2 = 0

∴ 2,1,1 are zeroes of polynomial.

let α = 2,β = 1 , ɣ = 1 are zeroes of polynomial then

α + β + ɣ = 4  

⇒ 1+ 2 + 1 = 4

αβ + αɣ + βɣ  = 5

⇒ 2 + 1 + 2 = 5

αβɣ = 2 .