document.write( "Question 1205621: f(x)=x^2+6x+20+k(x^2-3x-12) where k is real. Find value of k given that f(x) is a straight line \n" ); document.write( "
Algebra.Com's Answer #842532 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "f(x)=x^2+6x+20+k(x^2-3x-12)
\n" ); document.write( "f(x)=x^2+6x+20+kx^2-3kx-12k
\n" ); document.write( "f(x)=(x^2+kx^2)+(6x-3kx)+(20-12k)
\n" ); document.write( "f(x)=(1+k)x^2+(6-3k)x+(20-12k) \r
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\n" ); document.write( "\n" ); document.write( "f(x) is linear if and only if the x^2 coefficient is 0.
\n" ); document.write( "1+k = 0
\n" ); document.write( "k = -1 is the final answer.\r
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\n" ); document.write( "If k = -1, then,
\n" ); document.write( "f(x)=x^2+6x+20+k(x^2-3x-12)
\n" ); document.write( "f(x)=x^2+6x+20-1(x^2-3x-12)
\n" ); document.write( "f(x)=x^2+6x+20-x^2+3x+12
\n" ); document.write( "f(x)=(x^2-x^2)+(6x+3x)+(20+12)
\n" ); document.write( "f(x)=0x^2+9x+32
\n" ); document.write( "f(x)=9x+32
\n" ); document.write( "which proves f(x) is linear when k = -1.\r
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\n" ); document.write( "\n" ); document.write( "Answer: k = -1
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