How to Find the X Intercept of a Polynomial

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Finding the X intercept of a polynomial is something you do by graphing. Find the X intercept of a polynomial with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Hello. My name is Walter Unglaub, and this is how to find the x intercept of a polynomial. A polynomial is generally a function that has multiple terms that are grouped in the order of, the order of magnitude of the variable. So for example I could have f of x is equal to a, some constant, plus b x raised to the power of 1, plus c times x squared, etc. And depending on the values of these coefficients, my graph will take on different shapes. So the x intercept is another way of say the root of the function and it is essentially where the function goes to zero at or along the x axis. In this drawing you'll notice that there are 2 x intercepts and that corresponds to 2 roots. And generally the number of roots corresponds to the term in the polynomial that has the highest order of magnitude. So as an example, if I started with a function g of x is equal to a plus b x, this is polynomial, notice that all the coefficients for all the higher order of magnitude terms in x are equal to zero, all I have to do is set the function equal to zero and solve for x. So here I have zero is equal to a plus b x. Therefore, by using some simple algebra I find that x is equal to negative a divided b. So here there's just one root, one location of x where the function goes to zero. If I wanted to look at a polynomial that was quadratic in x, so I would have a plus b x plus c x squared, then I do the same thing. I set the function equal to zero and I solve for x. Because this particular polynomial is quadratic in x I simply use the quadratic formula. Which is for these coefficients minus b plus minus the square root of b squared minus 4 times the coefficient in front of the x square term which is c times the constant in the polynomial which is a, all divided by 2 times the coefficient in front of the x squared term. In this case it's c. And this is going to be equal to my x intercepts. And notice that there are two roots here, plus and minus. And this is due to the fact that this term is x squared. My name is Walter Unglaub and this is how to find the x intercept in a polynomial.

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