document.write( "Question 1108284: The quadratic function f is positive only on the intervals (−∞, 0) and (10, ∞). f has a minimum value of −100. Determine the coefficients of f.
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Algebra.Com's Answer #723294 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Since f(x) has the roots at x= 0  and  x= 10,\r\n" );
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document.write( "f(x) = k*(x-0)*(x-10) = kx*(x-10)  \r\n" );
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document.write( "at some real \"k\".\r\n" );
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document.write( "Since f(x) has the minimum -100,\r\n" );
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document.write( "-100 = f(5) = 5k*(5-10) = 5k*(-5) = -25k,\r\n" );
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document.write( "which implies  k =  = 4.\r\n" );
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document.write( "Thus f(x) = 4x*(x-10) = .\r\n" );
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