Question

if alfa and beta are the zeroes of the polynomial p(x) =x square-5x+7 then find
the polynomial whose zeroes are alfa square, beta square​

Answer 1

Step-by-step explanation:

 if alpha and beta are the zeros of 2x 2 5x 7 find the polynomial whose zeros are 2alpha 3beta and 3 alpha 2beta ...

Answer 2

Step-by-step explanation:

When roots are given, equation in quadratic form

x

2

−(α+β)x+αβ=0

Here roots are (2α+3β) and (3α+2β)

∴x

2

−(2α+3β+3α+2β)x+(2α+3β)(3α+2β)=0

x

2

−5(α+β)x+6α

2

+4αβ+4αβ+6β

2

=0

f(x)=2x

2

−5x+7

α+β=

2

5

, αβ=

2

7

∴α

2

+β

2

=(α+β)

2

−2αβ

=

4

25

−7=

4

−3

x

2

−5(

2

5

)x+6(−

4

3

)+13×

2

7

=0

∴2x

2

−50x−18+182=0

2x

2

−50x+164=0

∴x

2

−25x+82=0.