document.write( "Question 1017157: If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?\r
\n" ); document.write( "\n" ); document.write( "For the format: ax² + bx + c = 0 \r
\n" ); document.write( "\n" ); document.write( "Sum of the roots = - b/a \r
\n" ); document.write( "\n" ); document.write( "Product of the roots = c/a \r
\n" ); document.write( "\n" ); document.write( "given: (4 + i) and (4 - i) \r
\n" ); document.write( "\n" ); document.write( "8 = - b/a
\n" ); document.write( "17 = c/a \r
\n" ); document.write( "\n" ); document.write( "a = (- b)/8 = 1
\n" ); document.write( "- b = 8
\n" ); document.write( "b = - 8 \r
\n" ); document.write( "\n" ); document.write( "a = c/17 = 1
\n" ); document.write( "c = 17 \r
\n" ); document.write( "\n" ); document.write( "equation is: z² - 8z + 17 = 0 \r
\n" ); document.write( "\n" ); document.write( "check...do something \n" ); document.write( "

Algebra.Com's Answer #633495 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( " If 4 + I and 4 - I are roots of the equation z^2 + az + b = 0 find the value of a and the value of b?
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document.write( "Since the quadratic equation has the coefficient \"1\" as the leading coefficient (at ), then \r\n" );
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document.write( "z1 + z2 = -a,\r\n" );
document.write( "Z1*z2 = b.\r\n" );
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document.write( "Hence, a = (4+i)*(4-i) = 16 -  = 16 - (-1) = 16 + 1 = 17.\r\n" );
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document.write( "       b = (4+i) + (4-i) = 8.\r\n" );
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document.write( "That is all.\r\n" );
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