If alpha and beta are the zeroes of quadratic polynomial ax^2+bx+c , then find alpha^4+beta^4

1 answer:

5 0

Ill write A for alpha and B for beta.

AB = c/a and A + B = -b/a

A^4 + B^4 = (A^2 + B^2)^2 - 2A^2B^2

= [(A + B)^2 - 2AB] ^2 - 2A^2B^2

Plugging in the values for A+B and AB we get

A^4 + B^4 = [(-b/a)^2 - 2c/a]^2 - 2(c/a)^2

= (b^2 / a^2 - 2c / a)^2 - 2c^2/a^2

= (b^2 - 2ac)^2 - 2c^2
---------------- -----
a^4 a^2

= (b^2 - 2ac)^2 - 2a^2c^2
-----------------------------
a^4

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Step-by-step explanation:

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5 0

2 years ago

Read 2 more answers

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Answer:

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Step-by-step explanation:

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