Test your understanding of Vieta's formulas, symmetric identities, and reducible polynomials.
1. For $2x^2-5x+3=0$, find the sum and product of the roots. (2 marks)
2. If $\alpha,\beta,\gamma$ are roots of $x^3-2x^2+4x-1=0$, find $\alpha+\beta+\gamma$ and $\alpha\beta\gamma$. (2 marks)
3. If $\alpha,\beta$ are roots of $x^2-3x+2=0$, find $\alpha^3+\beta^3$. (2 marks)
4. Factorise $x^4-10x^2+9$ over the reals. (3 marks)