Let f(x) = 2x^3 + 3x^2 - 4x - 1 = 0.
Use the intermediate value theorem to determine whether the equation f(x) has any roots in the interval [0.2, 2].
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Practise this question\binom{n}{r} in terms of factorials.[1 mark]\binom{n}{r} = \binom{n}{n - r}.[3 marks]x^4 in \left(x^2 - \frac{3}{x}\right)^8.[5 marks](1 + x)^{2n} = (1 + x)^n (1 + x)^n, show that \binom{2n}{n} = c_0^2 + c_1^2 + c_2^2 + \dots + c_{n-1}^2 + c_n^2, where…[8 marks]x_1 = 0.6 as a first approximation of a root T of f(x), execute FOUR iterations of the Newton–Raphson method to obtain a second approximation,…[6 marks]More practice: the rest of this paper · more Roots of Equations questions · all CAPE Pure Mathematics Unit 2 past papers