Quick questions on Roots of polynomials: sums and products of roots, symmetric functions and new equations - OCR A-Level Further Maths A

3short 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 errors in the substitution direction?

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For new roots

\alpha + 2

you substitute

x \to x - 2

(the inverse), not

x \to x + 2

; getting the direction wrong reverses the shift.

What is q1?

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The quadratic

x^2 + 7x + 12 = 0

has roots

\alpha, \beta

. State

\alpha + \beta

and

\alpha\beta

. [2 marks]

What is q2?

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For a cubic with

\sum\alpha = 4

and

\sum\alpha\beta = 1

, find

\sum\alpha^2

. [2 marks]

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