Given : F(x)= x^3-8x^2+17x-4 : find the rational, irration, complex zeros. Write the f(x) in linear factor form

linear-factor-form

#1

given : F(x)= x^3-8x^2+17x-4 : find the rational, irration, complex zeros. Write the f(x) in linear factor form.

Answer:

First, note that 4 is a root. In fact, if you know little maths, you can see 4 is rational.

Exercise: Prove 4 is rational.

Now, use vanishing method. You have, F(X)= (X-4)(X^2 - 4X + 1)

Solving the quadratic equation by the formula that everyone knows, the roots are 2 + sqrt(3) and 2 - sqrt(3).

Exercise: Show that 2 + sqrt(3) and 2 - sqrt(3) are irrationals.

Now, rational and irrational are real numbers. So you have no complex root !!