2 the factor theorem

Question 1

How do you prove that there are exactly two real solutions to the equation -3y^6 +8y^4-9y^2+10=0

Answer 1

• Use a substitution of y^2= x

- Then solve for the values of x and then sub this into the original substitution to find the number of real solutions.

Question 2

How do you deduce the number of real solutions to 3tan^3 - 8tan^2+9tan-10=0

Answer 2

make tan=x then solve the equation for x and sub these back into tan=x and find the number of solutions

Question 3

What is the factor theorem?

Answer 3

x-a is a factor of f(x) if f(a) = 0

Question 4

How do you proceed if a question asks you to, without a calculator, work out roots.

Answer 4

-Find the first root through factor theorem then do the next through column division.