22M.2.AHL.TZ1.8

pestleMathematicsAAHLPaper 222M· sl-2-7-solutions-of-quadratic-equations-and-inequalities-discriminant-and-nature-of-rootssource ↗

Consider the equation $k x^{2} - (k + 3) x + 2 k + 9 = 0$ , where $k \in ℝ$ .

Write down an expression for the product of the roots, in terms of $k$ .

[1]

Hence or otherwise, determine the values of $k$ such that the equation has one positive and one negative real root.

[3]

Markscheme / solution

product of roots $= \frac{2 k + 9}{k}$ A1

[1 mark]

recognition that the product of the roots will be negative (M1)

$\frac{2 k + 9}{k} < 0$

critical values $k = 0, - \frac{9}{2}$ seen (A1)

$- \frac{9}{2} < k < 0$ A1

[3 marks]

Examiners’ report

[N/A]