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Exam-Style Questions on Polynomial RootsProblems on Polynomial Roots adapted from questions set in previous Mathematics exams. |
1. | IB Analysis and Approaches |
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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