Math, asked by AddiZaroo, 10 hours ago

if alpha and beta are the zeros of the quadratic polynomial f(x)= ax²+bx+c, then evaluate alpha⁴-beta⁴​

Answers

Answered by shivanshipatel982
0

Answer:

If α and β are zero of f(x)=ax

2

+bx+c. The evaluate α

4

×β

4

Note that we have

=(α+β)

4

4

4

+

4

C

1

α

3

β

1

+

4

C

2

α

2

β

2

+

4

C

3

α

1

β

1

3

Then, α

4

4

=(α+β)

4

−4(α

3

β

1

1

β

3

)−6α

2

β

2

=(α+β)

4

−4αβ(α

2

2

)−6(αβ)

2

Maxover, we have

α+β=−

a

b

and αβ=

a

c

Then,

α

4

4

=(−

a

b

)

4

−4(

a

c

)[(−

a

b

)

2

−2(

a

c

)]−6(

a

c

)

2

=

a

4

b

4

a

4c

(

a

2

b

2

)+8(

a

c

)

2

−6(

a

c

)

2

=

a

4

b

4

a

3

4b

2

c

+2

a

2

C

2

please brainliest mark

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