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Quick questions on Further algebra and functions: series, roots of polynomials and method of differences - Edexcel A-Level Further Maths

4short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is wrong sign for the root sum?
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For ax2+bx+cax^2 + bx + c the sum of roots is −ba-\frac{b}{a}, not ba\frac{b}{a}; remember the signs alternate with degree.
What is q1?
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Evaluate ∑r=1n(2r−1)\displaystyle\sum_{r=1}^{n} (2r - 1). [3 marks]
What is q2?
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The quadratic x2−5x+6=0x^2 - 5x + 6 = 0 has roots α,β\alpha, \beta. Find α2+β2\alpha^2 + \beta^2. [3 marks]
What is q3?
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Find a quadratic with roots α+2\alpha + 2 and β+2\beta + 2, where α,β\alpha, \beta are the roots of x2−6x+8=0x^2 - 6x + 8 = 0. [4 marks]

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