Question

If alpha and beta are zeroes of the quadratic polynomial x^2-5, then form a quadratic polynomial whose zeroes are 1+alpha and 1+beta​

Answer 1

Answer:

If the polynomial is x2 - 5, then to calculate the zeroes you would write:

x2 - 5 = 0

which leads to

x2 = -5

which yields solutions

x = +/- i√5 where i = √-1

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

Step-by-step explanation:

hope it's help you

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