Question

Solve 2cos^2x+cosx-1=0 for the interval [0, 2π)

Answer 1

This is a quadratic equation in \(\cos x\).

Answer 2

You have to factor this just like you would a "regular" polynomial.

Answer 3

You get nice and easy factors too! Any ideas?

Answer 4

I have no idea what to do.

Answer 5

To make it easier to understand, substitute \(\cos x\) with \(u\).
Then solve the quadratic equation for \(u\).
Then substitute back \(\cos x \) for \(u\), and solve the trig equations.

Answer 6

The above is an idea of what to do.
Do you know how to solve a simple quadratic equation by factoring?

Answer 7

No.

Answer 8

Help?

Answer 9

Do you know how to factor a trinomial, such as 2x^2 + x - 1 ?