Find all the zeros of the following function.
step by step
f(x)=x^4+3x^2-4
To find the zeros of the function f(x) = x^4 + 3x^2 - 4, we need to solve the equation f(x) = 0.
Step 1: Set f(x) = 0.
x^4 + 3x^2 - 4 = 0
Step 2: We can use factoring or the quadratic formula to solve for the zeros. In this case, we have a quadratic expression in terms of x^2.
Let's substitute x^2 = y to simplify the equation:
(y)^2 + 3(y) - 4 = 0
Step 3: Factor the quadratic expression.
(y + 4)(y - 1) = 0
Step 4: Set each factor equal to zero and solve for y.
y + 4 = 0 or y - 1 = 0
Solving these equations, we get:
y = -4 or y = 1
Step 5: Substitute y = x^2 back into our equations.
For y = -4:
x^2 = -4
Since the square of a real number cannot be negative, there are no real solutions for this equation.
For y = 1:
x^2 = 1
Taking the square root of both sides, we get:
x = 1 or x = -1
So, the zeros of f(x) = x^4 + 3x^2 - 4 are x = 1 and x = -1.