Question

if alpha and beta are the zeros of a quadratic polynomial f of x = 2 x square - 5 x + 1 find the polynomial whose zeros are 2 alpha + 3 Beta and 3 alpha + 2 beta. ( Without the concept of 'i')​

Answer 1

Heya

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Required quadratic equation in x is

x² - ( 5× ( Alfa + Beta ) ) + 6( Alfa² + Beta² ) + 13 Alfa × Beta

=>

Alfa + Beta = 5/2

And

Alfa × Beta = 1/2

=>

x² - ( 5× ( 5/2 )x + 6 ( 25/4 ) +11 ( 1/2)

=>

x² - (25/2 )x + 47×3/2

OR

x² -25x + 141=0

Answer 2

It could help you.

And it can be solve more