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AS 1 Pure Mathematics

Quick questions on Roots of polynomial equations: sums and products of roots and forming new equations - CCEA A-Level Further Maths

5short 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 forming a new equation?
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Solving the equation when you should not. Questions usually say "without solving" or have awkward roots on purpose. Use the symmetric functions and identities rather than the quadratic formula.
What is wrong substitution direction?
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For new roots y=α+1y = \alpha + 1, you substitute x=y−1x = y - 1 (because the old root x=αx = \alpha corresponds to the new root). Substituting x=y+1x = y + 1 shifts the wrong way.
What is q1?
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The roots of x2+3x−10=0x^2 + 3x - 10 = 0 are α\alpha and β\beta. Find α+β\alpha + \beta and αβ\alpha\beta. [2 marks]
What is q2?
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Using those values, find α2+β2\alpha^2 + \beta^2. [2 marks]
What is q3?
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The roots of x3+4x2−x+6=0x^3 + 4x^2 - x + 6 = 0 are α,β,γ\alpha, \beta, \gamma. Write down αβγ\alpha\beta\gamma. [1 mark]

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