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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