Question

if alpha and beta are the zeros of a polynomial x square - 1 then find the polynomial whose zeros are 2 alpha divided by beta and 2 Beta / Alpha

Answer 1

Hi Mate !!

Here's ur ans :-

Given equation :- x² - 1

Let's factorise it by using identity :-

a² - b² = ( a - b ) ( a + b )

x² - 1 = 0

x² - ( 1 )² = 0

( x + 1 ) ( x - 1 ) = 0

• ( x + 1 ) = 0

x = ( - 1 )

• ( x - 1 ) = 0

x = 1

So,

# For new equation having Zeros as :-

So, the Zeros of new equation are ( - 2 ) and ( - 2 )

• Sum of the Zeros

( - 2 ) + ( - 2 )

- 2 - 2

= ( - 4 )

• Product of Zeros :-

( - 2 ) × ( - 2 )

= 4

♯ To form the quadratic equation we have formula as :-

x² - ( Sum of Zeros )x +(Product of Zeros )

Putting value in the formula :+

x² - ( - 4 )x + ( 4 ) = 0

x² + 4x + 4 = 0

So, the required quadratic equation is :

-x² + 4x + 4 = 0