I was needing help with approximating zeros in the problem f(x)=-3x^3-4x^2+x-3. I know I'm suppose to start off by replacing F(x) with zero to make the problem F(0)=-3x^3-4x^2+x-3. But it won't factor and thats where I'm having trouble. Thanks...
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Approximating Zeros of f(x) = -3x^3 - 4x^2 + x - 3
- Thread starter lil hoots
- Start date
Re: Approximating Zeros
>by replacing F(x) with zero to make the problem F(0)=-3x^3-4x^2+x-3.
You have not replaced F(x) with zero. You replaced x with zero.
If you replace F(x) with zero, you get 0=-3x^3-4x^2+x-3.
If you replace x with zero, you get F(0)=-3(0)^3-4(0)^2+0-3 = -3.
Now, what zeros are you talking about? Where the curve crosses the x-axis in which case y=0 or where the curve crosses the y-axis in which case x=0?
I approximate a zero at pretty close to x=-1 4/5 (-1.8).
>by replacing F(x) with zero to make the problem F(0)=-3x^3-4x^2+x-3.
You have not replaced F(x) with zero. You replaced x with zero.
If you replace F(x) with zero, you get 0=-3x^3-4x^2+x-3.
If you replace x with zero, you get F(0)=-3(0)^3-4(0)^2+0-3 = -3.
Now, what zeros are you talking about? Where the curve crosses the x-axis in which case y=0 or where the curve crosses the y-axis in which case x=0?
I approximate a zero at pretty close to x=-1 4/5 (-1.8).
Re: Approximating Zeros
The "zeros" of a polynomial function is where the curve crosses the x-axis.
Are you allowed to use a graphing calculator?
If so, graph the function and look at the table of values obtained. Inspect where the y value changes sign with respect to x. This is the interval in which you will find your zero (there is only one real zero). Inspection tells me it lies between -1 and -2.
You can use trial and error approx to enter x values into your function to approach f(x) = 0, but the CALC key on your TI will be much faster. Press CALC (2nd TRACE) on your TI and choose option 2 (zero). Move your spider using the left arrow key to just above the x-axis on your curve. Enter. That's your left bound. Move the spider using the right arrow to just below the x-axis of your curve. Enter. That's your right bound. Enter one last time and your zero is -1.818869 (irrational). Using the rational roots theorem tells you there are no rational roots. There are also 2 imaginary roots.
The "zeros" of a polynomial function is where the curve crosses the x-axis.
Are you allowed to use a graphing calculator?
If so, graph the function and look at the table of values obtained. Inspect where the y value changes sign with respect to x. This is the interval in which you will find your zero (there is only one real zero). Inspection tells me it lies between -1 and -2.
You can use trial and error approx to enter x values into your function to approach f(x) = 0, but the CALC key on your TI will be much faster. Press CALC (2nd TRACE) on your TI and choose option 2 (zero). Move your spider using the left arrow key to just above the x-axis on your curve. Enter. That's your left bound. Move the spider using the right arrow to just below the x-axis of your curve. Enter. That's your right bound. Enter one last time and your zero is -1.818869 (irrational). Using the rational roots theorem tells you there are no rational roots. There are also 2 imaginary roots.