1.4: Relations between the roots of a quadratic

4PM1/2/June/2022 — Question 5 · 9 marks

The roots of the quadratic equation
2x2+(6+2p)x+2p=02x^2+(6+2p)x+2p=0
are α\displaystyle \alpha and β\displaystyle \beta.
(a) Write down an expression in terms of p\displaystyle p for
(i) α+β\displaystyle \alpha+\beta,
(ii) αβ\displaystyle \alpha\beta.
(2)
(b) Show that
(α−β)2=9+2p+p2.(\alpha-\beta)^2=9+2p+p^2.
(4)
Given that α−β=3\displaystyle \alpha-\beta=3,
(c) find the possible values of p\displaystyle p.
(3)