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04 - QUADRATIC EQUATIONS Page 1 ( Answers at the end of all questions ) ( 1 ) The value of a for which the sum of the squares of the roots of the equation x 2 - ( a - 2 ) x - a - 1 = 0 assume the least value is ( a ) 1 ( b ) 0 ( c ) 3 ( d ) 2 [ AIEEE 2005 ] ( 2 ) If the roots of the equation x 2 - b x + c = 0 be two consecutive integers, then b 2 - 4 c equals ( a ) - 2 ( b ) 3 ( c ) 2 ( d ) 1 [ AIEEE 2005 ] ( 3 ) If both the roots of the quadratic equation x 2 - 2kx + k 2 + k - 5 = 0 are less than 5, then k lies in the interval ( a ) ( 5, 6 ] ( b ) ( 6, ) ( c ) ( - , 4 ) ( d ) [ 4, 5 ] [ AIEEE 2005 ] ( 4 ) Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation ( a ) x 2 + 18x + 16 = 0 ( b ) x 2 - 18x + 16 = 0 ( c ) x 2 + 18x - 16 = 0 ( d ) x 2 - 18x - 16 = 0 [ AIEEE 2004 ] ( 5 ) If ( 1 - p ) is a root of quadratic equation x 2 + px + ( 1 - p ) = 0, then the roots are ( a ) 0, 1 ( b ) - 1, 1 ( c ) 0, - 1 ( d ) - 1, 2 [ AIEEE 2004 ] ( 6 ) If one root of the equation x 2 + px + 12 = 0 is 4, while the equation x 2 + px + 12 = 0 has equal roots, then the value of q is ( a ) 4 49 ( b ) 12 ( c ) 3 ( d ) 4 [ AIEEE 2004 ] ( 7 ) The number of real solutions of the equation x 2 - 3 l x l + 2 = 0 is ( a ) 2 ( b ) 4 ( c ) 1 ( d ) 3 [ AIEEE 2003 ]

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04 - QUADRATIC EQUATIONS Page 2 ( Answers at the end of all questions ) ( 8 ) The value of ‘ a ’ for which one root of quadratic equation ( a 2 - 5a + 3 ) x 2 + ( 3a - 1 ) x + 2 = 0 is twice as large as the other is ( a ) 3 2 ( b ) 3 2 - ( c ) 3 1 ( d ) 3 1 - [ AIEEE 2003 ] ( 9 ) If roots of the equation x 2 - 5x + 16 = 0 are α, β and roots of the equation x 2 + px + q = 0 are α 2 + β 2 and 2 β α , then ( a ) p = 1 and q = - 56 ( b ) p = - 1 and q = - 56 ( c ) p = 1 and q = 56 ( d ) p = - 1 and q = 56 [ AIEEE 2002 ] ( 10 ) If α and β be the roots of the equation ( x - a ) ( x - b ) = c, c 0, then the roots of the equation ( x - α ) ( x - β ) = c are ( a ) a and c ( b ) b and c ( c ) a and b ( d ) ( a + b ) and ( b + c ) [ AIEEE 2002, IIT 1992 ] ( 11 ) If one root of the equation x 2 + px + q = 0 is square of the other, then for any p and q it will satisfy the relation ( a ) p 3 - q ( 3p - 1 ) + q 2 = 0 ( b ) p 3 - q ( 3p + 1 ) + q 2 = 0 ( c ) p 3 + q ( 3p - 1 ) + q 2 = 0 ( d ) p 3 + q ( 3p + 1 ) + q 2 = 0 [ IIT 2004 ] ( 12 ) If x 2 + 2ax
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