15 If α and β are the zeroes of the quadratic polynomial f(x) = x2 2x + - Maths - Polynomials

Question

15 If α and β are the zeroes of the quadratic polynomial
f(x) = x 2 –
2x + 3 find a polynomial whose zeroes are α + 2 and
β + 2

Brijendra Pal · Accepted Answer

Hi,
If α,β are zeros of the polynomial x2 - 2x +
3 then

α + β = 2

αβ = 3

If α + 2 , β +2 are zeros of the polynomial then
x2 - ( α + 2 + β +2 )x + (α + 2)(β
+ 2) = 0

= x2 - ( α + β + 4 )x + (αβ +
2(α + β) + 4) = 0

= x2 -6x + 11 = 0

15. If α and β are the zeroes of the quadratic polynomial f(x) = x 2 – 2x + 3 find a polynomial whose zeroes are α + 2 and β + 2.