\(\alpha\) and \(\beta\)

Level pending

The two roots of the quadratic equation \(x^2+4x+1=0\) are \(\alpha\) and \(\beta\). If \(f(x)=0\) is a quadratic equation for \(x\) that has two roots \(2\alpha+\beta\) and \(\alpha+2\beta\), what is the value of \(f(1)\)?

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