document.write( "Question 1088451: If a,b,c i.e the coefficients of the quadratic equation ax^2+bx+c=0 are in A.P and the one root of this given equation is 2, then find the other root?
\n" ); document.write( "a)3/4
\n" ); document.write( "b)-3/4
\n" ); document.write( "c)-5/4
\n" ); document.write( "d)-5/2
\n" ); document.write( "My attempt.
\n" ); document.write( "Since this is a competitive exam question,I first tried to solve mentally. i.e by putting a=1 which suggested me that b=1+d and c=1+2d where d=common difference
\n" ); document.write( "Now I made an equation,
\n" ); document.write( "x^2+(root+2)+2*root=0
\n" ); document.write( "compare with above made equation
\n" ); document.write( "x^2+bx+c=0 since a=1 i putted
\n" ); document.write( "then b=root+2 and c=2*root, and then it became like unsolvable for me!!! Please help,thanks!!! \n" ); document.write( "
Algebra.Com's Answer #702717 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "If a,b,c i.e the coefficients of the quadratic equation ax^2+bx+c=0 are in A.P and the one root of this given equation is 2, then find the other root?
\n" ); document.write( "a)3/4
\n" ); document.write( "b)-3/4
\n" ); document.write( "c)-5/4
\n" ); document.write( "d)-5/2
\n" ); document.write( "My attempt.
\n" ); document.write( "Since this is a competitive exam question,I first tried to solve mentally. i.e by putting a=1 which suggested me that b=1+d and c=1+2d where d=common difference
\n" ); document.write( "Now I made an equation,
\n" ); document.write( "x^2+(root+2)+2*root=0
\n" ); document.write( "compare with above made equation
\n" ); document.write( "x^2+bx+c=0 since a=1 i putted
\n" ); document.write( "then b=root+2 and c=2*root, and then it became like unsolvable for me!!! Please help,thanks!!!
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document.write( "You are given that\r\n" );
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document.write( "\"ax%5E2+%2B+bx+%2B+c\" = 0.                            (1)\r\n" );
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document.write( "Since a, b and c are AP, b = \"%28a%2Bc%29%2F2\".       (2)  \r\n" );
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document.write( "    It is a characteristic property of any AP.\r\n" );
document.write( "    See the lesson One characteristic property of arithmetic progressions in this site.\r\n" );
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document.write( "In (1), replace b by \"%28a%2Bc%29%2F2\" and divide both sides of (1) by \"a\". You will get an equivalent equation\r\n" );
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document.write( "\"x%5E2+%2B+%281%2F2+%2B+c%2F%282a%29%29x+%2B+%28c%2Fa%29\" = 0.                     (3)\r\n" );
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document.write( "Since x= 2 is the root of this equation (Given !), you can substitute x= 2 into (3). You will get\r\n" );
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document.write( "\"2%5E2+%2B+%281%2F2+%2B+c%2F%282a%29%29%2A2+%2B+%28c%2Fa%29\" = 0,   or\r\n" );
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document.write( "\"4+%2B+1+%2B+c%2Fa+%2B+c%2Fa\" = 0,   or\r\n" );
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document.write( "\"2%2A%28c%2Fa%29\" = -5   and finally  \"c%2Fa\" = \"-5%2F2\".\r\n" );
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document.write( "Now your equation (3) takes the form\r\n" );
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document.write( "\"x%5E2+%2B+%281%2F2+-+5%2F4%29x+-+5%2F2\" = 0,   or, which is the same,\r\n" );
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document.write( "\"x%5E2+-+%283%2F4%29x+-+5%2F2\" = 0.                          (4)\r\n" );
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document.write( "    You may check that x= 2 is the root of this equation.\r\n" );
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document.write( "    By the way, you actually found THE COEFFICIENTS of your original equation (1)\r\n" );
document.write( "       under the assumption that the leading coefficient \"a\" is equal to 1.\r\n" );
document.write( "       These coefficients are 1, \"-3%2F4\" and \"-5%2F2\", and you can check that they form an AP.\r\n" );
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document.write( "Now you can solve your equation (4) and to find the other root.\r\n" );
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document.write( "I will leave it to you.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "          H a p p y   l e a r n i n g  ! !\r
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\n" ); document.write( "\n" ); document.write( "I am glad that I am still able to solve competitive problems !!\r
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\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Mathematical induction and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "You have, actually, three free of charge online textbooks in Math in this site \r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK\r
\n" ); document.write( "\n" ); document.write( "    - GEOMETRY - YOUR ONLINE TEXTBOOK \r
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\n" ); document.write( "\n" ); document.write( "The level of these textbooks is exactly \"SHCOOL +\" adequate to the level of students who really want to know the school math
\n" ); document.write( "and wish participate in school Math competitions.\r
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\n" ); document.write( "\n" ); document.write( "            As I did in my youth school years . . . \r
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