Question

If α and β are the zeroes of the quadratic polynomial f(x) = x² -px + q ,
prove that $\frac{ \alpha ^{2}}{ \beta ^{2} } + \frac{ \beta ^{2}}{ \alpha ^{2} } = \frac{ p^{4} }{q^{2} } - \frac{4 p^{2} }{q} + 2$

Answer 1

hi friend,

<>we know that œ+ß=p

<>ϧ=q

now,let us find the value of œ²+ß²

<>(œ+ß)²-2œß

<>p²-2q

now ,let's find the value of œ⁴+ß⁴

→(œ²+ß²)²-2œ²ß²

→(p²-2q)²-2q²

→p⁴+4q²-4p²q-2q²

→p⁴+2q²-4p²q

now,the question is

→(œ⁴+ß⁴)/œ²ß²


→(p⁴+2q²-4p²q)/q²

→p⁴/q²+2-4p²/q


hence proved..


I hope this will help u ;)