Question

if alpha and bita are zeros of quadratic polynomial 4x^2+4x+1 then form a quadratic polynomial whose zeros are 2alpha and 2bita​

Answer 1

Step-by-step explanation:

4x^2+4x+1=0

4x^2+2x+2x+1=0

2x(2x+1)+1(2x+1)=0

(2x+1)(2x+1)=0

x=-1/2

alpha=-1/2

beta=-1/2

alpha×beta=c/a

-1/2×(-1/2)=c/a

1/4=c/a

So,

c=1

a=4

alpha+beta=-b/a

-1/2-1/2=-b/a

-1=-b/a

1=b/a

a=b

a=b=4

So the new equation is:

4x^2+4x+1=0

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