A LevelFurther MathsEdexcelCore PureExam QuestionsFurther Algebra & FunctionsRoots of Polynomials

Roots of Polynomials (Edexcel A Level Further Maths: Core Pure): Exam Questions

Exam code: 9FM0

26 mins3 questions
1a7 marks

straight f left parenthesis z right parenthesis equals 3 z cubed plus p z squared plus 57 z plus q

wherespace p and q are real constants.

Given that 3 minus 2 square root of 2 straight i is a root of the equation straight f left parenthesis z right parenthesis equals 0, show all the roots of straight f left parenthesis z right parenthesis equals 0 on a single Argand diagram,

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1b
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Find the value ofspace p and the value of q.

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2
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The roots of the equation

x cubed minus 2 x squared plus 4 x minus 5 equals 0

are p comma space q and r.

Without solving the equation, find the value of

(i)   2 over p plus 2 over q plus 2 over r

(ii)   left parenthesis space p space – space 4 right parenthesis left parenthesis q space – space 4 right parenthesis left parenthesis r space – space 4 right parenthesis

(iii)   p cubed space plus space q cubed space plus space r cubed

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3
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The roots of the equation

x cubed minus 8 x squared plus 28 x minus 32 equals 0

are alpha comma space beta and gamma

Without solving the equation, find the value of

(i)   1 over alpha plus 1 over beta plus 1 over gamma

(ii)   left parenthesis alpha plus 2 right parenthesis left parenthesis beta plus 2 right parenthesis left parenthesis gamma plus 2 right parenthesis

(iii)   alpha squared plus beta squared plus gamma squared

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