Question

1. If and are the zeros of the polynomial 2x2 – 4x + 5. Form the polynomial where zeros are 1+α/β and 1+β/α​

Answer 1

Given polynomial -

2x² - 4x + 5

α + β = { -b / a } = 2

αβ = { c / a } = ( 5 / 2 )

Zeroes of new polynomial -

1+α/β and 1+β/α

Sum of Zeroes -

=> 2 + ( α + β ) / ( αβ )

=> 2 + { 2 } / { 2 / 5 }

=> 7

Product of Zeroes -

( 1+α/β )( 1+β/α )

=> => 2 + ( α + β ) / ( αβ )

=> 2 + { 2 } / { 2 / 5 }

=> 7

P ( x ) = x² - ( sum of Zeroes ) + ( product of Zeroes )

=> P ( x ) = x² - 7x + 7

This is the required answer .

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AddiTiOnaL InFoRmAtIon +

α + β = { -b / a }

αβ = { c / a }

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