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

Question

this is a question of class 10, of chapter polynomial

Answer 1

Hi Neha,

 

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