Given that α and β are the roots of the quadratic equation 3x² - 5x + 1 = 0:
(a) Write down the values of (α + β) and αβ. [2 marks]
(b) Find the value of:
(i) α² + β² [3 marks]
(ii) α³ + β³ [4 marks]
(c) Find the quadratic equation whose roots are (2α + β) and (α + 2β), expressing your answer in the form px² + qx + r = 0, where p, q and r are integers. [6 marks]

Question

Given that α and β are the roots of the quadratic equation 3x² - 5x + 1 = 0:
(a) Write down the values of (α + β) and αβ. [2 marks]
(b) Find the value of:
    (i) α² + β²  [3 marks]
    (ii) α³ + β³  [4 marks]
(c) Find the quadratic equation whose roots are (2α + β) and (α + 2β), expressing your answer in the form px² + qx + r = 0, where p, q and r are integers. [6 marks]

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Answer

A) null

Answer

B) null

Answer

C) null

Answer

D) null

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