Question

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

Answer 1

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