## Exam-Style Question on Polynomial Roots## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 635. This question is similar to one that appeared on an IB AA Higher paper in 2022. The use of a calculator is allowed.

Consider the equation \( (k-4)x^2 — \frac{kx}{5} + 4(2-k) = 0 \), where \( k \in \mathbb{R} \).

(a) Write down an expression for the product of the roots. in terms of \(k\).

(b) Hence or otherwise. determine the values of \(k\) such that the equation has one positive and one negative real root.

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