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Finding Zeroes of a polynomial
The below given fact will also be useful on occasion in determining the zeroes of a polynomial.
Fact
If P (x) is a polynomial & we know that P (a) = 0 and P (b) = 0 then somewhere among a and b is a zero of P ( x ) .
According to this fact if we evaluate the polynomial at two points & one of the evaluations provides a positive value (that means the point is above the x-axis) & the other evaluation provides a negative value (that means the point is below the x-axis), then the single way to get from one point to the other is to go through the x-axis. Or, in other terms, the polynomial ought to have a zero, as we know that zeroes are where a graph touches or crosses the x-axis.
Notice that this fact doesn't tell us what the zero is, it just tells us that one will present. Also, note that if both of the evaluations are +ve or both evaluations are -ve there may or may not be a zero among them.
Horizontal Shifts These are quite simple as well though there is one bit where we have to be careful. Given the graph of f ( x ) the graph of g ( x ) = f ( x + c ) will be t
if im working out a problem that say 16 - t over 10 = -8 what be the answer
y=2x 2x
I am trying to figure out this answer f(x) = -3/4x + 4. but think I am getting it all wrong
2x+y/x+3y=-1/7and 7x+36y=47/3 hence find p if xy=p=x/y
show that -b/b-a may be properly changed to b/a-b...show steps
In a yacht race the second leg was half the length of the first leg, the third leg was two-thirds of the second leg, and the last leg was twice the length of the second leg. If the
The difference of two numbers is 18. The larger number is four more than twice the smaller. What are the numbers?
600tyou
2xsquare + 5x -12
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