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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.
Here we'll be doing is solving equations which have more than one variable in them. The procedure that we'll be going through here is very alike to solving linear equations that i
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for what value of x is \2x-3\-4
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y = 4 - 3x /1 + 8x for x. Solution This one is very alike to the previous instance. Here is the work for this problem. y + 8xy = 4 - 3x 8xy + 3x = 4 - y X(8 y +3)
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