Year 11 Maths - Methods Polynomials

Quartic And Other Polynomial Functions

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Questions

Question 1

28685

Solve \({x^4} - 27x = 0\)

Answer

\(x = 0,{\rm{ }}x = 3\)

Worked Solution

\begin{align}
&\begin{aligned}
x^{4}-27x&=0 \\
x\left(x^{3}-27\right)&=0
\end{aligned}\\
&\begin{aligned}
x=0 \text { or } x^{3}-27&=0 \\
x^{3}&=27 \\
x&=\sqrt[3]{27} \\
&=3
\end{aligned}\\
&\therefore x=0,\; x=3
\end{align}

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