-
Looking for HSC notes and resources? Check out our Notes & Resources page
Polynomials (1 Viewer)
- Thread starter Casper_18
- Start date
gurmies
Drover
Question 2
(A)
+\gamma\delta(\alpha+\beta)\\\\=\alpha\beta(\gamma+\delta)+\alpha\beta(\alpha+\beta)[Since\,\,\alpha\beta=\gamma\delta] \\\\ =\alpha\beta(\alpha+\beta+\gamma+\delta)=p(\alpha\beta)=r \\\\ \prod \alpha_{i}=\alpha\beta\gamma\delta=(\alpha\beta)^{2}=s \\\\ \therefore \alpha\beta = \sqrt{s} \\\\ \therefore p\sqrt{s}=r \Rightarrow r^{2}=sp^{2})
(B)
=p \Rightarrow \alpha+\beta=\frac{p}{2} \\\\ \sum \alpha\beta_{i}=\alpha\beta+\alpha\gamma+\alpha\delta+\beta\gamma+\beta\delta+\gamma\delta=\alpha(\gamma+\delta)+\beta(\gamma+\delta)+\alpha\beta+\gamma\delta \\\\ = (\alpha+\beta)(\gamma+\delta)+\alpha\beta+\gamma\delta=(\alpha+\beta)^{2}+\alpha\beta+\gamma\delta=q \Rightarrow \alpha\beta+\gamma\delta=q-\frac{p^{2}}{4} \\\\ \sum \alpha\beta\gamma_{i}=\alpha\beta\gamma+\alpha\beta\delta+\alpha\gamma\delta+\beta\gamma\delta=\alpha\beta(\gamma+\delta)+\gamma\delta(\alpha+\beta) \\\\ = \alpha\beta(\alpha+\beta)+\gamma\delta(\alpha+\beta)=(\alpha+\beta)(\alpha\beta+\gamma\delta)=r \Rightarrow (\frac{p}{2})(q-\frac{p^{2}}{4})=r \\\\ \therefore p^{3}-4pq+8r=0)
(A)
(B)
Last edited:
Timothy.Siu
Prophet 9
yeah they put this in our first task for ext2, i had no idea how to do it, but i see its just heavy algebra now
Yeah, it is a hard question. I suppose I just have to do enough of them so I know how to do as many as possible automatically