document.write( "Question 165601: Given 5x^4-3x^3+ax^2+bx-7 determine a and b so i is a zero of the quartic (Hint:Use synthetic or long division). Please help me, I just can't find the answer!!! \n" ); document.write( "
Algebra.Com's Answer #122081 by ankor@dixie-net.com(22740)\"\" \"About 
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Given 5x^4-3x^3+ax^2+bx-7 determine a and b so i is a zero of the quartic (Hint:Use synthetic or long division).
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\n" ); document.write( "Assume you mean, \"determine a and b so 1 is a zero\"
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\n" ); document.write( "Using synthetic division:
\n" ); document.write( "..._________________________
\n" ); document.write( " 1 | 5 - 3 + a + b - 7
\n" ); document.write( ".........+ 5 + 2 +(2+a)+(2+a+b);using this to form an equation with -7
\n" ); document.write( ".....--------------------------
\n" ); document.write( "......5 + 2+(2+a)+(2+a+b)
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\n" ); document.write( "2 + a + b - 7 = 0; the remainder is 0
\n" ); document.write( "a + b - 5 = 0
\n" ); document.write( "a + b = 5
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\n" ); document.write( "Try the integers a=2,b=3
\n" ); document.write( "..._______________________-
\n" ); document.write( "1 | 5 - 3 + 2 + 3 - 7
\n" ); document.write( ".........+ 5 + 2 + 4 + 7
\n" ); document.write( "......--------------------------
\n" ); document.write( "......5 + 2 + 4 + 7 + 0
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\n" ); document.write( "5x^4 - 3x^3 + 2x^2 + 3x - 7; is our solution
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\n" ); document.write( "It's interesting that the integers a=1; b=4 will also work and vice versa
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\n" ); document.write( "Hope this made sense to you. \n" ); document.write( "
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