1.

If alpha and ßare zeroes of the quadraticpolynomial 4x2 +4x + 1, thenform quadraticpolynomial whose zeroes are2 alpha and 2 beta​

Answer»

Step-by-step explanation:

solve this lets divide the QUADRATIC equation by 4 such that we have it in the FORM x

2

+(α+β)x+αβ

so after dividing by 4 we have

4

4x

2

+4x+1

x

2

+x+

4

1

So we haveα+β=1 ...................(1)

andαβ=

4

1

..................(2)

So if ZEROES to the new quadratic equation are 2α and 2β, then

2α+2β=2(α+β)

=2(1)=2 .................... Using (1)

and,

2α×2β=4αβ

=4×

4

1

=1 .................... Using (2)

So the new quadratic equation with its roots 2αand2β will be

x

2

+(2α+2β)x+2α×2β

Putting the values, the equation would be,

x

2

+2x+1


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