2025 Beatty Sec 3 EOY Q8

It is given that \(\mathrm{f}(x)=x^3+ax^2+bx+28\), where \(a\) and \(b\) are constants, has a factor of \(x+4\) and leaves a remainder of \(30\) when divided by \(x-1\).

1. Find the values of \(a\) and \(b\).[4]
2. Using the values of \(a\) and \(b\) found in (a), show that the equation \(\mathrm{f}(x)=0\) has only one real root.[3]