Question

If α and β are zeroes of a quadratic polynomial x^2 - 5, then form a quadratic polynomial
whose zeroes are 1+α and 1+β.​

Answer 1

Answer:

We are to calls these zeroes α and β. So, α = i√5 and β = -i√5.

We now want to form a polynomial with roots 1 + α and 1 + β. This yields the equation,

[x - (1 + α)][x - (1 + β)] = 0

Multiplying we get

x2 -(1 + β)x - (1 + α)x + (1 + α)(1 + β) = 0

or

x2 - (2 + α + β)x + (1 + α)(1 + β) = 0

or

x2 - (2 + i√5 - i√5) + (1 + i√5)(1 - i√5) = 0

or

x2 - 2x + 6 = 0