document.write( "Question 1107265: Given one of the roots of the equation 2x power of 2 + 1 = h-5x is four times to other root. Find the value oh h \n" ); document.write( "

Algebra.Com's Answer #722367 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Given one of the roots of the equation 2x power of 2 + 1 = h-5x is four times to other root. Find the value oh h
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document.write( "The given equation\r\n" );
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document.write( " = \r\n" );
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document.write( "is the same as\r\n" );
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document.write( " = 0,\r\n" );
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document.write( "which is equivalent to\r\n" );
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document.write( " = 0.     (1)\r\n" );
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document.write( "Let one root be r.\r\n" );
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document.write( "Then the other root is 4r, according to the condition.\r\n" );
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document.write( "The sum of the roots is equal to the coefficient at \"x\" in the equation (1) taken with the opposite sign (the Vieta's theorem). Hence\r\n" );
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document.write( "r + 4r = ,   or   5r = ,   which implies  r = .\r\n" );
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document.write( "Now substitute  into equation (1) and take into account that  is the root. You will get\r\n" );
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document.write( " = 0.\r\n" );
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document.write( "It is your equation to find h.   Simplify and solve for h:\r\n" );
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document.write( " -  = ,\r\n" );
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document.write( "-1 = ,\r\n" );
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document.write( "h-1 = -2  ====>  h = -2 + 1 = -1.\r\n" );
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document.write( "Answer.  h = -1.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Ignore the solution by @josgaritmetic, since it leads to nowhere.\r
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