IB Maths AA HL AA 2.2 Quadratics questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper
Paper 1, no calculatorPaper 2, calculator
Difficulty
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Question 1

Paper 1, no calculatorMedium6 marks

For real pp consider the equation

x2−2px+p+2=0,x∈R.x^2-2px+p+2=0,\qquad x\in\mathbb R.
(a)

Determine the values of pp for which the equation has (i) two distinct real roots, (ii) two equal real roots, and (iii) no real roots.

[4]
(b)

Hence, when p=3p=3 solve

x2−2px+p+2≤0.x^2-2px+p+2\leq 0.
[2]

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