Solve the equation on the interval (0,2\pi) where - \cos^2x+5\cos x+3=0 Find all angles x on...


Solve the equation on the interval {eq}(0,2\pi) {/eq} where:

{eq}- \cos^2x+5\cos x+3=0 {/eq}

Find all angles {eq}x {/eq} on this interval?

Quadratic Formula

The solutions to a general quadratic equation in one variable i.e. {eq}ax^2+bx+c =0 {/eq} are {eq}x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a} {/eq}.

The term {eq}D = b^2-4ac {/eq} is called the determinant of the quadratic equation.

For two distinct real roots to exist, {eq}D>0 {/eq}.

Answer and Explanation:

Let {eq}\cos x = t,\,\,-1\leq t\leq 1 {/eq} then the given equation becomes {eq}-t^2+5t+3 = 0 {/eq}.

Substituting {eq}a = -1 {/eq}, {eq}b =...

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Learn more about this topic:

Solving a Trigonometric Equation Graphically

from Precalculus: High School

Chapter 17 / Lesson 6

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