Q4. a) Can the Intermediate Value Theorem be applied to show that there is a root of the
equation x^5 -x³ + 3x - 5= 0 in the given interval ]1,2[? If yes, apply it.
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Defining the function
F(x) = X^5-x³+3x-5=0
The function f(x) is continous on the closed interval [1,2] as polynomial.
f(1) = 1^5 - 1³ + 3*1 - 5 = -2 < 0
f(2) = 2^5 - 2³ + 3(2) - 5 = 25 > 0
By the intermediate value Theorem f must have a zero between 1 and 2.
Hence the intermediate value Theorem can be applied to show that there is a root of the equation.
as given in question.⟵⟵(๑¯◡¯๑)
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