Question

if alpha and beta are roots of the polynomial x square minus 25, find the polynomial who's root are 1 plus aplpha and 1 plus beta

Answer 1

HEY FRIEND

HERE IS YOUR ANSWER

=x²-25

=(x)²-(5)²

[USING a²-b²=(a+b)(a-b) ]

=(x+5)(x-5)

x+5=0

x= -5

α= -5

x-5=0

x=5

β=5

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ROOTS OF THE POLYNOMIAL ARE :

α= -5

β= 5

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NEW ROOTS :

=1+α

=1-5

= -4

AND

=1+β

=1+5

=6

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THE NEW ROOTS ARE -4 AND 6

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SUM OF ROOTS :

= (1+α)+(1+β)

= -4+6

=2

PRODUCT OF ROOTS:

=(1+α)(1+β)

= -4×6

= -24

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REQUIRED POLYNOMIAL :

=x²-(sum of roots)x+(product of roots)

=x²-(2)x+(-24)

=x²-2x-24

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SO THE REQUIRED POLYNOMIAL IS x²-2x-24

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HOPE THIS HELPS YOU ☺

Answer 2

it Is your answer ......
♥♥♥thank you♥♥♥......


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