2025 Tanjong Katong Secondary School Prelims A Math Paper 2
The term containing the highest power of \(x\) in the polynomial \(f(x)\) is \(2x^4\). Two of the roots of the equation \(f(x)=0\) are \(\frac{1}{2}\) and \(-3\). Given that \(x^2+1\) is a quadratic factor of \(f(x)\), find an expression for \(f(x)\) in descending powers of \(x\).[3]
Find the value of \(k\) for which \(x^2+(k-1)x+k^2-16\) is exactly divisible by \(x-3\) but not divisible by \(x+4\).[4]
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