Question

h3y guys hru ✌

if alpha and beta are the zeroes of the quadratic polynomial p(x)=2x^2-5x+7, find the polynomial whose zeroes are (2 alpha+3 beta) and (2beta+3alpha).​

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Answer 1

Answer:

see the attachment ok

Step-by-step explanation:

hope it's help u

Answer 2

Answer:

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.

hope it hlps uu mahraj ji