Question
Let α, β be roots of x²-5x+6=0. Find α³+β³-3αβ.
This question was previously asked in
UPTET 2026 Paper 2 Social Studies Question Paper (3-Jul-2026) (Shift 1)
The correct answer is
17
The quadratic equation is \(x^2 - 5x + 6 = 0\), with roots \(\alpha\) and \(\beta\).
By comparing coefficients, \(\alpha + \beta = 5\) and \(\alpha\beta = 6\).
Using the identity \(\alpha^3 + \beta^3 = (\alpha+\beta)^3 - 3\alpha\beta(\alpha+\beta)\):
\(\alpha^3 + \beta^3 = 5^3 - 3(6)(5) = 125 - 90 = 35\).
So, \(\alpha^3 + \beta^3 - 3\alpha\beta = 35 - 3(6) = 35 - 18 = 17\).
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