Question

If alpha and beta are the zeroes of a quadratic polynomial 4x2+4x+1 then form quadratic polynomial whose zeroes are 2 alpha and 2 beta

Answer 1

HEY FRIEND ☺

HERE IS YOUR ANSWER

=4x²+4x+1

=4x²+2x+2x+1

=2x(2x+1)+1(2x+1)

=(2x+1)(2x+1)

2x+1=0
x= -1/2
α=-1/2

2x+1=0
x= -1/2
β=-1/2

SO α= -1/2 and β=-1/2

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QUADRATIC POLYNOMIAL WHOSE ZEROES ARE 2α AND 2β

2α=2×-1/2= -1

2β=2×-1/2= -1

SUM OF ZEROES :

=2α+2β

= -1-1

= -2

PRODUCT OF ZEROES:

=2α×2β

= -1×-1

=1

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REQUIRED POLYNOMIAL :

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

=x²-(-2)x+1

=x²+2x+1

SO THE REQUIRED POLYNOMIAL IS x²+2x+1

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HOPE THIS HELPS YOU ☺

Answer 2

Answer:

Step-by-step explanation: