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how many times does the red curve either touch the x axis or cross the x axis?
is it 4?
yes 4 times
so there are 4 roots (aka 4 x intercepts)
does it also apply to this question ? which is another problem :The points plotted below are on the graph of a polynomial. Some of the roots to this polynomial are integers. Which of the following x-values are roots of the polynomial? Check all that apply. A. x = -2 B. x = 0 C. x = 1 D. x = -5 E. x = -4 F. x = -3
yeah you'll follow the same steps. Draw a curve through the points and see where the x intercepts are
instead of listing out how many there are, you list out what the actual roots are
i drawn the line and what should i be looking at because it has the 4 roots like the previous question , or should i be looking at where the each dot of the x-axis are plotted ?
they want you to report where on the number line (the horizontal number line, aka the x axis) the curve crosses
for example, say we had this curve |dw:1450408845871:dw| the curve in my example above goes through -2 on the x axis, so -2 is a root of this function
so its where the dot touches the number so in mine one of them would be -3
-3 is one root, yes
-2 has a dot there but it doesnt touch is that consider a root aswell as 1 on the positive side?
-2 looks like another root
on the positive side i see a 1 but the dot is above and a little to the side of 1 thats is that consider a root ? i only see 3 roots overall but i am not sure if i am right on the 1 ?
yes, 1 looks like a root as well
-3, -2, and 1 look like the three roots well actually there is a 4th root slightly after x = 1
this is all educated guesswork really
is it 0 ?
0 isn't a root
if theres 4 roots then it will be either -5 or -4 but i dont see how will it have 4 roots if theres no roots close to those two numbers
like I said, if you draw a curve through all the points, this curve looks like it goes through x = -3, x = -2 and x = 1 on the x axis the fourth root it goes through is some number between 1 and 2 (like 1.3 or something)
because in my answer options it only has 3 roots that i found theres no anser of a 1.3 i know what your reffering too i se the dot between them to but in my options i believe theres only 3 since they arent giving me the 4th one
that 4th root (the one between x = 1 and x = 2) won't be reported
i seen your graph and yes i agree it doesnt give it to me in the answer options
because the only options i have left is -5 , -4, and 0
It's definitely not -5
not -4 or not 0 either
so i guess it only 3 roots for the problem they gave me
yeah ignore that root between x = 1 and x = 2
yes , i agree with you & for this problem same rules apply The points plotted below are on the graph of a polynomial. Which of the following x-values is the best approximation of a root of the polynomial? Check all that apply. A. x = 6 B. x = -1.1 C. x = 1 D. x = -1.7 E. x = 4.3 F. x = 2.4
i know that one of them is -1.1 correct ?