Show that there is a root of the equation below between1 and 2.4x3 - 6x2 + 3x - 2 =0solution let f(x) = 4x3 - 6x2 + 3x - 2. we arelooking for a solution of the given equation, that is, a numberc between 1 and 2 such that f(c) = . therefore we take a = , b = , and n = in the intermediate value theorem. wehavef(1) =4 - 6 +3 - 2 = -1 < 0f(2) = 32 - 24 +6 - 2 = 12 > 0thus f(1) < 0 0a root must lie between and . a calculation gives, by trial anderror, f(1.22) =-0.007008 < 0f(1.23) = 0.056068 > 0so a root lies in the interval (1.22, 1.23).