Moderate -0.3 This is a standard FP1 roots transformation question requiring application of sum/product formulas. Students find α+β=-2 and αβ=5 from the first equation, then compute α²+β²=(α+β)²-2αβ=-6 and α²β²=(αβ)²=25 to get p=6, q=25. While it requires multiple steps and is Further Maths content, it's a routine textbook exercise with a well-established method, making it slightly easier than average overall.
**In this question you must show detailed reasoning.**
The equation \(x^2 + 2x + 5 = 0\) has roots \(\alpha\) and \(\beta\). The equation \(x^2 + px + q = 0\) has roots \(\alpha^2\) and \(\beta^2\).
Find the values of \(p\) and \(q\). [3]
**In this question you must show detailed reasoning.**
The equation $x^2 + 2x + 5 = 0$ has roots $\alpha$ and $\beta$. The equation $x^2 + px + q = 0$ has roots $\alpha^2$ and $\beta^2$.
Find the values of $p$ and $q$. [3]
\hfill \mbox{\textit{OCR FP1 AS 2017 Q1 [3]}}