document.write( "Question 1181921: Let f(x) = x^2 + kx and g(x)=x + k. The graphs of f and g intersect at two distinct points. Find the value(s) of k. \n" ); document.write( "

Algebra.Com's Answer #811888 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "Let f(x) = x^2 + kx and g(x)=x + k. The graphs of f and g intersect at two distinct points. Find the value(s) of k.
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document.write( "It means that the function f(x) - g(x) has two distinct real roots.\r\n" );
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document.write( "f(x) - g(x) = x^2 + kx - x - k = x^2 + (k-1)x - k.\r\n" );
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document.write( "The discriminant is  d = \" b^2 - 4ac \" = (k-1)^2 - 4*1*(-k) = k^2 - 2k + 1 + 4k = k^2 + 2k + 1 = (k+1)^2.\r\n" );
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document.write( "The function f(x) - g(x) has two distinct real roots if and only if the discriminant is positive.\r\n" );
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document.write( "It is true if and only if   k =/= -1.\r\n" );
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document.write( "ANSWER.  The graphs f and g intersect at two distinct points for any real number k different from -1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and carefully explained.\r
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