Chapter: Quadratic Equations· Mathematics Part 1 (Algebra)
Answer: \(k = 9\) or \(k = -9\)
Let the roots be \(\alpha\) and \(2\alpha\).
Product: \(\alpha \times 2\alpha = \dfrac{c}{a} = 18 \Rightarrow 2\alpha^2 = 18 \Rightarrow \alpha = \pm 3\).
Sum: \(\alpha + 2\alpha = 3\alpha = -\dfrac{b}{a} = k\).
If \(\alpha = 3\): \(k = 9\) (roots 3, 6). If \(\alpha = -3\): \(k = -9\) (roots −3, −6).