Edexcel IALGeneralGeneral Applications8 Marks
The equation `2x³ - x² + px + q = 0`, where `p` and `q` are constants, has roots `α`, `β` and `γ`. Given that `α = 2`, `β = -3`. (a) Show that `γ = 1/2`. (b) Find the value of `p` and the value of `q`. (c) Find the value of `α² + β² + γ²`.
- (a)Show that `\gamma = 1/2`.[2]
- (b)Find the value of `p` and the value of `q`.[4]
- (c)Find the value of `α² + β² + γ²`.[2]
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- B1 for `α+β+γ = -(-1)/2` or `1/2`.
- M1 for `2 + (-3) + \gamma = 1/2`.
- A1 for `\gamma = 1/2` (cso).
- M1 for using product of roots formula or sum of products of roots taken two at a time formula.
- A1 for `p = -13`.
- A1 for `q = 6`.
- M1 for using `α²+β²+γ² = (α+β+γ)² - 2(αβ+αγ+βγ)` (allow slips, e.g. sign error).
- A1 for `53/4` or `13.25`.
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