ou will need three roots for this, so we have
Let x = -30, -10 and +20
So the factors will be (x+30)(x+10)(x-20)
The divide it to 100, this will help bring the peak up and down
So the polynomial function R(x) will become
1/100 * (x+30)(x+10)(x-20)
R(x) = 1/100 * (x+30)(x+10)(x-20)
Finding the X-intercept:
Let R(x) = 0 and solve for x.
1/100 * (x+30)(x+10)(x-20) = 0
x = -30, -10, 20 are the x-intercepts.
The 1st feature of the polynomial function is that its graph is continuous, it is, in the graph of the polynomial function has no breaks. The 2nd feature is that the graph of the polynomial function has only smooth, rounded turns.
From the problem establishes that we can create the sample polynomial to be used in our explanations, we can say that this polynomial function is:
[tex]R(x) = -2x^{4} + 2x^{2}[/tex]
To find the x-intercepts of R(x) set R(x) equal to zero and solve for x, so:
Set R (x) = 0
[tex]0 = -2x^{4} + 2x^{2}[/tex]
[tex]-2x^{4} + 2x^{2} = 0[/tex]
Remove common monomial factor :
[tex]-2x^{4} + 2x^{2} = 0[/tex]
Factor out:
[tex]-2x^{2} (x-1)(x+1)=0[/tex]
So the real zero are:
x = 0
x = 1
x = -1
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