Question

If α and β are the zeroes of the polynomial ax ​2 + bx + c then evaluate 1/ α 4 ​ + 1/β ​4 ​

Answer 1

α,β are the zeros of the quadratic polynomial ax²+bx+c=0.
Then, α+β=-b/a and α×β=c/a
1/α⁴+1/β⁴
=(β⁴+α⁴)/(αβ)⁴
={(α²)²+(β²)²}/(c/a)⁴
={(α²+β²)²-2α²β²}/(c/a)⁴
=a⁴[{(α+β)²-2αβ}²-2(αβ)²]/c⁴
=a⁴[{(-b/a)²-2c/a}²-2(c/a)²]/c⁴
=a⁴{(b²/a²-2c/a)²-2c²/a²}/c⁴
=a⁴ (b⁴/a⁴-4b²c/a³+4c²/a²-2c²/a²)/c⁴
=(b⁴-4ab²c+4a²c²-2a²c²)/c⁴
=(b⁴-4ab²c+2a²c²)/c⁴

Answer 2

Hey plz refer the answer in the ATTACHMENT

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Happy learning!