2.14: Completing the square and a quartic equation

0606/23/O/N/18 — Question 3 · 8 marks

(i)
Write 8+7x−x28 + 7x - x^{2} in the form a−(x−b)2a - (x - b)^{2}, where aa and bb are constants.
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(ii)
Hence state the maximum value of 8+7x−x28 + 7x - x^{2} and the value of xx at which it occurs.
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(iii)
Using your answer to part (i), or otherwise, solve the equation 8+7z2−z4=08 + 7z^{2} - z^{4} = 0.
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