Year 11 (2026) Maths Extension 1 (2026)
Polynomials
Sums and Products of Zeroes
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Questions
Question 1
122813
The roots of \(x^2+p x+q=0\) are \(\alpha\) and \(\beta\). Express each of the following in terms of \(p\) and \(q\).
(i) \(\dfrac{1}{\alpha}+\dfrac{1}{\beta}\)
(ii) \(\alpha^2+\beta^2\)
(iii) \((\alpha+1)(\beta+1)\)
Part a:
\(\dfrac{p}{q}\)
\(-\dfrac{p}{q}\)
Correct
\(-\dfrac{q}{p}\)
\(\dfrac{q}{p}\)
Part b:
\(p^2-2q\)
Correct
\(p^2+2q\)
\(p^2-q\)
\(2q-p^2\)
Part c:
\(q+p+1\)
\(q-p-1\)
\(q-p+1\)
Correct
\(p-q+1\)
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