CAIE IGCSE Additional Math 2.3 Use Discriminant Conditions Questions

Practise Cambridge IGCSE Additional Mathematics by applying discriminant conditions for distinct, equal or absent roots, tangency and non-intersection.

Exam points

Use the discriminant to determine whether a quadratic has two real roots, equal roots or no real roots.
Apply discriminant inequalities to find parameter values for real roots or distinct roots.
Relate discriminant conditions to line-curve intersections, tangency and non-intersection.

[Maximum number: 5]

2 In this question,k is a constant.

It is given that $2 x^{2}+(3 k-2) x+k=0$ has roots that are real and distinct.

Find the set of possible values of k .

$(3 k-2)^{2}-4(2)(k)\left[{ }^{*} 0\right]$
Uses $b^{2}-4 a c$
* could be any inequality sign or = $9 k^{2}-20 k+4\left[{ }^{*} 0\right]$
Correctly simplifies to 3-term quadratic
(9 k-2)(k-2)
FT Factorises or solves their 3-term
quadratic
Critical values $\frac{2}{9}, 2$ $k<\frac{2}{9} k>2$ $k<\frac{2}{9}$ k>2
Mark final answer

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CAIE IGCSE Additional Math 2.3 Use Discriminant Conditions Questions question 1