how do i solve this polynomial inequality, (x-4)(x+2)>0?
Stacey Warren - Expert brainly.com
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find where it is zero first and then make a little chart for numbers before and after each zero
k so x=4 and x=-2
-2 comes before 4
so choose any number before -2 to see what happens to the factors btw -inf..-2
choose any number in btw -2 and 4 to see what happens to the factors between -2..4
choose any number after 4 to see what happens to the factors after 4..inf
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simple enough. thanks
x-4 > 0
x > 4 and
x + 2 > 0
x < -2
therefore, the solutions are (-infinity, -2) union (4, +inifinity)
so lets the first interval i have listed choose a number before -2
a negative time a negative is a positive so (-inf,-2) is part of your answer
now 2nd interval choose a number between -2 and 4
a negative times a positive is negative so (-2,4) is not apart of our answer
now last interval choose a number btw 4..inf like 5
a postive times a postive= positive so (4,inf) is apart of our answer
so our answer is x is an element of (-inf,-2)U(4,inf) notice i didnt include the -2 and 4 because the inequality did not have a line underneath
i didn't realize someone had posted i was so busy lol
what about x^2-5x+4>0
would it then be x-1>0 and x-4>0?
i would do (x-4)(x-1)>0
x=4 and x=1 is when LHS is 0
so 1 comes before 4
so choose a number before 1 like 0
we have 0-1=-1 and 0-4=-4 (-1)(-4)>0 so (-inf,1) is part of our answer
now choose a number btw 1 and 4 like 2
we have 2-1=1 and 2-4=-2 so 1(-2)=-2<0 so (1,4) is not part of answer
now we choose our final test number after 4 like 100
we have 100-1=99 and 100-4=96 and (99)(96)>0 so (4,inf) is apart of our answer
our answer is (-inf,1)U(4,inf)
so you choose a point before the first term. if it is true in the equation all numbers before that term will be included? then you choose a number between the two terms and if it is not true no numbers between the terms will be included? then you choose a number after the larger term, if it is true all terms larger than the greater term will be true?