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Question 480371: let f(x)=x squared-4x+3. The values of x for which f(x) is less than or equal to 0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! let f(x)=x squared-4x+3. The values of x for which f(x) is less than or equal to 0
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f(x)=x^2-4x+3≤0
write equation in factored form
f(x)=(x-3)(x-1)≤0
number line with zeros
<....+....1.....-.....3.....+.......>
You can see that when x>3, f(x)>0
When x<1, f(x)>0
When x≥1 or x≤3, f(x)≤0
Solution: [1, 3]
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note: while this problem can be solved almost by inspection, a general method to use in determining sign of f(x) in each interval between zeros is to first determine the sign of the interval between the most positive zero and infinity, then moving left thru the other zeros. The sign will switch every time you go thru a zero of odd multiplicity, eg, 1,3,5,etc, as illustrated by this problem. The more conventional method taught in most schools is to make a chart, but this is much more time consuming.
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