I need help with finding the zeros of the function: x^4+10x^2+9.
Factor it first to..
(x^2+9)(x^2+1)=0
x^2=-9 x^2=-1
x=+-3j x=+-j
where j is the sqrt of -1. There are no real zeroes.
but there are complex zeros
To find the zeros of the function f(x) = x^4 + 10x^2 + 9, you need to solve the equation f(x) = 0. Here's how you can do it:
Step 1: Start by moving all terms to one side of the equation, so you have x^4 + 10x^2 + 9 = 0.
Step 2: Notice that the equation is in the form of a quadratic in terms of x^2. You can define a new variable, let's say u = x^2. By substituting u back into the equation, we get u^2 + 10u + 9 = 0.
Step 3: Solve the quadratic equation u^2 + 10u + 9 = 0 using factoring, completing the square, or the quadratic formula.
Factoring: (u + 1)(u + 9) = 0
Setting each factor equal to zero gives: u + 1 = 0 or u + 9 = 0
Solving these equations, we get: u = -1 or u = -9
Step 4: Substitute the values of u back into the equation u = x^2 to find the values of x.
Substituting u = -1 gives: x^2 = -1
Since taking the square root of a negative number is not possible in the real number system, there are no real solutions for x.
Substituting u = -9 gives: x^2 = -9
Taking the square root of both sides, we get: x = ±√(-9)
Again, since we are working with real numbers, there are no real solutions for x.
Therefore, the equation x^4 + 10x^2 + 9 = 0 has no real zeros.