how in the world do you solve this...
4cos^2x -3 =0
add three to both sides, divide both sides by four, then, take the square root of both sides.
f(x)=x'3+7x'2-x-7 find Zeros,solutions, answers, roots,and x-intercept
To find the zeros, solutions, answers, roots, and x-intercepts of the function f(x) = x^3 + 7x^2 - x - 7, you need to set the function equal to zero and solve for x.
1. Set the function f(x) equal to zero:
x^3 + 7x^2 - x - 7 = 0
2. To solve this equation, you can try factoring, using the Rational Root Theorem, or using numerical methods such as graphing or approximation.
3. Let's start with factoring. It's always a good idea to check for any possible rational roots first. In this case, the possible rational roots are factors of the constant term (-7) divided by factors of the leading coefficient (1).
The factors of -7 are ±1 and ±7, and the factors of 1 are ±1. So the possible rational roots are: ±1, ±7.
Try substituting these possible rational roots into the equation. If any of them make the equation equal to zero, then that value is a zero or root.
4. By trying the possible rational roots, we find that x = 1 is a zero of the equation. This means (x - 1) is a factor of the equation.
Using long division or synthetic division, divide the given equation by (x - 1) to find the other factor(s) and simplify the equation. The result will be a quadratic equation.
(x^3 + 7x^2 - x - 7) ÷ (x - 1) = x^2 + 8x + 7
5. Now, we have a quadratic equation: x^2 + 8x + 7 = 0.
6. To solve the quadratic equation, you can use factoring, completing the square, or the quadratic formula. In this case, factoring is the most convenient.
Factoring the quadratic equation gives you: (x + 1)(x + 7) = 0.
7. Setting each factor equal to zero, you have:
x + 1 = 0 or x + 7 = 0
Solving these equations separately gives you the roots:
x = -1 or x = -7
8. Therefore, the zeros, solutions, answers, roots, and x-intercepts of the function f(x) = x^3 + 7x^2 - x - 7 are x = -1 and x = -7.