If alpha and beta are zeroes …
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Sia ? 6 years, 4 months ago
α,β are zeros of ax2+bx+c
{tex}\mathrm{Then}\;\mathrm\alpha+\mathrm\beta=-\frac{\mathrm b}{\mathrm a}\;\mathrm{and}\;\mathrm{αβ}=\frac{\mathrm c}{\mathrm a}{/tex}
α4 + β4= (α2 + β2)2 - 2α2β2
=((α + β)2 - 2αβ)2 - (2αβ)2
{tex}={\left[ {\left( { - \frac{b}{a}} \right) - 2\left( {\frac{c}{a}} \right)} \right]^2} - \left[ {2{{\left( {\frac{c}{a}} \right)}^2}} \right]{/tex}
{tex} = {\left[ {\frac{{{b^2} - 2ac}}{{{a^2}}}} \right]^2} - \frac{{2{c^2}}}{{{a^2}}}{/tex}
{tex} = \frac{{{{\left( {{b^2} - 2ac} \right)}^2} - 2{a^2}{c^2}}}{{{a^4}}}{/tex}.
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