document.write( "Question 967928: http://www.algebra.com/tutors/students/your-answer.mpl?question=967815
\n" ); document.write( "I am asking how did u get the discriminant less than zero. Did the question says tell . Please explain. \n" ); document.write( "

Algebra.Com's Answer #591600 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
Not being in your class, I have no idea how you were expected to solve this problem. The ways you can solve a problem vary, depending on what you have learned so far. A fifth grader may have only one way to solve it, but a colleg professor may be able to think of many different ways.
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\n" ); document.write( "Maybe you were expected to try different integer values for p,
\n" ); document.write( "and graph the resulting functions using a graphing calculator.
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\n" ); document.write( "Maybe the expected approach is the one the other poster(s) tried to explain,
\n" ); document.write( "which apparently made no sense to you.
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\n" ); document.write( "Let's try this a different way. Maybe you'll like it better.
\n" ); document.write( "The original question was:
\n" ); document.write( "\"Find the smallest integer p such that x^2-2x+p is always greater than 3\".
\n" ); document.write( " $\"x%5E2-2x%2Bp=x%5E2-2x%2B1%2Bp-1=%28x%5E2-2x%2B1%29%2B%28p-1%29=%28x-1%29%5E2%2B%28p-1%29\"$
\n" ); document.write( "We know that a square, like $\"%28x-1%29%5E2\"$ is never negative.
\n" ); document.write( " $\"%28x-1%29%5E2%3E=0\"$
\n" ); document.write( "For $\"x=1\"$ , $\"%28x-1%29%5E2=0\"$ and $\"x%5E2-2x%2Bp=x%5E2-2x%2B1%2Bp-1=%28x-1%29%5E2%2B%28p-1%29=p-1\"$ .
\n" ); document.write( "Otherwise $\"x%5E2-2x%2Bp=x%5E2-2x%2B1%2Bp-1=%28x-1%29%5E2%2B%28p-1%29\"$ is greater than $\"p-1\"$ .
\n" ); document.write( " $\"p-1\"$ is the minimum value for $\"x%5E2-2x%2Bp=x%5E2-2x%2B1%2Bp-1=%28x-1%29%5E2%2B%28p-1%29\"$ .
\n" ); document.write( "We need $\"p-1%3E3\"$ <---> $\"p-1%2B1%3E3%2B1\"$ <---> $\"p%3E4\"$ .
\n" ); document.write( "Because the problem asks for the smallest $\"red%28integer%29\"$ that makes x^2-2x+p always greater than 3,
\n" ); document.write( "and the smallest integer $\"p\"$ such that $\"p%3E4\"$ is $\"5\"$ ,
\n" ); document.write( "the answer is $\"highlight%285%29\"$ .
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\n" ); document.write( "Does your teacher expect you to talk about the discriminant of a quadratic equation and/or the quadratic formula?
\n" ); document.write( "Maybe, but I agree with professor Peter Alfeld, that there is no need to memorize such things.
\n" ); document.write( "(I do remember them, because they made me memorize such things,
\n" ); document.write( "and maybe you will experience the same,
\n" ); document.write( "because most people believe that just for expediency,
\n" ); document.write( "you should memorize stuff that you could deduce on your own). \n" ); document.write( "

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