Determine all roots of the function: f(x) = 10x(x^2+4x+3)
I just want to know how it’s done, our teacher just thrusted this our way and I’ve never seen a problem like that before.
You want 10x(x^2 + 4x + 3) = 0
factors of the quadratic should be obvious to you:
10x(x+1)(x+3) = 0
set each of the three factors equal to zero and solve for x
Thanks Reiny! I had just figured that out but thanks for confirming.
To determine the roots of the function f(x) = 10x(x^2 + 4x + 3), we first need to factorize the quadratic expression inside the parentheses. Once we have factored the expression, we can set each factor equal to zero and solve for x to find the roots.
Factoring the quadratic expression (x^2 + 4x + 3):
We are looking for two numbers that multiply to give 3 and add to give 4. These numbers are 1 and 3. Therefore, we can rewrite the quadratic expression as:
x^2 + 4x + 3 = (x + 1)(x + 3)
Now, let's set each factor equal to zero and solve for x:
x + 1 = 0
x = -1
x + 3 = 0
x = -3
The solutions to the equation are x = -1 and x = -3. These are the roots of the function f(x) = 10x(x^2 + 4x + 3).