document.write( "Question 476572: its all about non linear inequalities. (x-5)(x-4) is greater than or equal to 0. \n" ); document.write( "
Algebra.Com's Answer #326780 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
easiest way to answer this is to graph it.
\n" ); document.write( "\"graph%28400%2C400%2C-10%2C10%2C-20%2C20%2C%28x-5%29%2A%28x-4%29%29\"
\n" ); document.write( "that's if you have the graphing software that makes it easy.
\n" ); document.write( "from the graph, it looks like this equation will be less than 0 between 4 and 5.
\n" ); document.write( "that stands to reason.
\n" ); document.write( "since this is a quadratic equation that has already been solved for the roots, it should be easy to determine what points in this equation are above 0 or below 0 or at 0.
\n" ); document.write( "the equation you have to work with is:
\n" ); document.write( "(x-5)*(x-4) = 0
\n" ); document.write( "by setting the expression equal to 0, you are looking for the roots.
\n" ); document.write( "the roots becomes:
\n" ); document.write( "x = 4 and x = 5
\n" ); document.write( "those are the zero points of the graph.
\n" ); document.write( "you multiply the factors together to get the original quadratic equation that gave you (x-5)*(x-4.
\n" ); document.write( "(x-5)*(x-4) = x^2 - 4x -5x + 20
\n" ); document.write( "combine like terms and you get:
\n" ); document.write( "x^2 - 9x + 20
\n" ); document.write( "if you set this equal to 0, then it becomes the standard form of the quadratic equation.
\n" ); document.write( "you get x^2 - 9x + 20 = 0
\n" ); document.write( "the standard form of the quadratic equation is ax^2 + bx + c = 0
\n" ); document.write( "this makes:
\n" ); document.write( "a = 1
\n" ); document.write( "b = -9
\n" ); document.write( "c = 20
\n" ); document.write( "the min/max point of the quadratic equation is given by the equation:
\n" ); document.write( "x = -b/2a
\n" ); document.write( "this becomes:
\n" ); document.write( "x = -(-9)/2) which becomes:
\n" ); document.write( "x = 4.5
\n" ); document.write( "That's the x value of the min/max point.
\n" ); document.write( "the y value of the min/max point is given by:
\n" ); document.write( "y = f(4.5)
\n" ); document.write( "you replace x with 4.5 in the equation and you get:
\n" ); document.write( "y = x^2 -9x + 20 which becomes:
\n" ); document.write( "y = (4.5)^2 -9*4.5 + 20 which becomes:
\n" ); document.write( "y = -.-025
\n" ); document.write( "your min/max point is at the (x,y) coordinates of (4.5,-.025).
\n" ); document.write( "now you want to determine whether this is a min point or a max point.
\n" ); document.write( "this is because you didn't see the graph i just showed you above.
\n" ); document.write( "you haven't even drawn the graph yet.
\n" ); document.write( "you're working just from the equation.
\n" ); document.write( "you look at the exponent of the x^2 term.
\n" ); document.write( "if it is positive then the graph points down and opens up.
\n" ); document.write( "if it is negative then the graph points up and opens down.
\n" ); document.write( "if the graph points down, then the min/max point is a min point.
\n" ); document.write( "if the graph points up, then the min/max point is a max point.
\n" ); document.write( "the graph is pointing down because the coefficient of the x^2 term is positive.
\n" ); document.write( "that would be the a in ax^2 which was equal to 1.
\n" ); document.write( "so your graph is point down.
\n" ); document.write( "the roots of the eqution are at x = 4 and x = 5
\n" ); document.write( "the min point is negative.
\n" ); document.write( "it will stay negative between the roots and it will be positive outside of the roots.
\n" ); document.write( "your equation is therefore >= 0 when:
\n" ); document.write( "x < 4 or x > 5\r
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