Jack C. answered • 18d
Make Math, Coding & Chemistry Click - Clear Explanations!
Hi Lewis! There are two ways you can go about finding the real zeros of a function:
The first way to find the real zeros is graphically. The real zeros or real roots of a polynomial function are the x-intercepts of the graph. If you are to take this function and graph it in a graphing calculator, you can then look and see where the graph is intersecting the x-axis and record those x values.
The second way to find the real zeros is by the Rational Zeros Theorem. If the polynomial function does have rational zeros, they will be a ratio of the last constant at the end of the function and of the leading coefficient.
so in this case, if we use the second method, we can take the "invisible" 1 that is in front of the x^2 and the -6 at the end. Possible rational zeros are factors of 6 divided by factors of 1: ±1, ±2, ±3, ±6. If we go ahead and start plugging these values into the function, we want to see if any of these numbers come back as 0.
This polynomial is particularly ugly and when testing these values, none of them will return the 0. Where normally if it did. Then you can go on to do polynomial division or synthetic division if possible to factor down this polynomial, set all of the factors = 0 and solve. Your best bet is to graph it and look at where it is crossing the x-axis and use the approximation:
x ≈ -3.732
x ≈ 1.000
I hope this helps a little on later problems!
