Find the exact solutions of the given equation in the interval [0, 2π).
A)
B)
C)
D)x = 0

Question

Find the exact solutions of the given equation in the interval [0, 2π). ​ 
A)​ 
B)​ 
C)​ 
D)​x = 0

Quizplus · Accepted Answer

The equation is:

cos^2(x) + cos(x) - 6 = 0

We can solve for cos(x) by using the quadratic formula:

cos(x) = (-1 ± sqrt(1 + 4(6)))/2
cos(x) = (-1 ± sqrt(25))/2

cos(x) = -3/2 or cos(x) = 2

Since cosine is only defined between -1 and 1, the only valid solution in the interval [0, 2π) is when cos(x) = 2.

However, there are no real values of x that satisfy this equation, so there are no solutions in the given interval.

Therefore, the answer is C, which indicates that there are no solutions in the given interval.

Find the Exact Solutions of the Given Equation in the Interval