document.write( "Question 1092372: Show that the roots of the equation (x-p)(x-q)=2 are real and distinct for all real values of p and q. \n" ); document.write( "

Algebra.Com's Answer #706981 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "1.  The quadratic function f(x) = (x-p)*(x-q)  is zero  at  x = p  (and x= q),  and goes \r\n" );
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document.write( "    to infinity as  x ---> infinity  or  x ---> - infinity.\r\n" );
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document.write( "    Hence, there is a value of x, where the function f(x) takes the intermediate value of 2:  f(x) = 2.\r\n" );
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document.write( "    So, the equation f(x) really has the roots.\r\n" );
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document.write( "2.  The roots can not be x= p  or  x= q,  since at these values the finction is zero (and, therefore, can not be 2).\r\n" );
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