Quadratic equation | IITJEE MAINS(AIEEE) PREVIOUS YEAR TOPICWISE QUESTION WITH SOLUTION | Quadratic equation

Quadratic equation

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Question no. 1

If the sum of the roots of the quadratic equation ax² + bx + c = 0 is equal to the sum of the squares of their reciprocals, then are in (2003)

looks_one Arithmetic progression

looks_two Geometric progression

looks_3 Harmonic progression

looks_4Arithmetic−Geometric−progression

Option 1. 0

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Question no. 2

The number of real solutions of the equation x² − 3 |x| + 2 = 0 is (2003)

looks_one 2

looks_two 4

looks_3 3

looks_4 1

option

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Question no. 3

The value of ‘a’ for which one root of the quadratic equation (a² − 5a + 3) x² + (3a − 1) x + 2 = 0 is twice as large as the other, is (2003)

looks_one 2/3

looks_two -2/3

looks_3 1/3

looks_4 -1/3

option

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Question no. 4

Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation (2004)

looks_one x² + 18x + 16 = 0

looks_two x² −18x −16 = 0

looks_3 x² + 18x −16 = 0

looks_4 x² −18x + 16 = 0

option

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Question no. 5

If (1 – p) is a root of quadratic equation x² + px + (1− p) = 0 , then its roots are (2004)

looks_one 0, 1

looks_two -1, 2

looks_3 0, -1

looks_4 -1, 1

option

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Question no. 6

If one root of the equation x² + px + 12 = 0 is 4, while the equation x² + px + q = 0 has equal roots, then the value of ‘q’ is (2004)

looks_one 49/4

looks_two 4

looks_3 3

looks_4 12

option

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Question no. 7

If 2a + 3b + 6c =0, then at least one root of the equation ax² + bx + c = 0 lies in the interval (2004)

looks_one (0,1)

looks_two (1,2)

looks_3 (2,3)

looks_4 (1,3)

option

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Question no. 8

The value of α for which the sum of the squares of the roots of the equation x² – (a – 2)x – a – 1 = 0 assume the least value is (2005)

looks_one 1

looks_two 0

looks_3 3

looks_4 2

option

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Question no. 9

If roots of the equation x² – bx + c = 0 be two consecutive integers, then b² – 4c equals (2005)

looks_one -2

looks_two 3

looks_3 2

looks_4 1

option

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Question no. 10

If both the roots of the quadratic equation x² – 2kx + k² + k – 5 = 0 are less than 5, then k lies in the interval (2005)

looks_one (5, 6]

looks_two (6, ∞)

looks_3 (-∞, 4)

looks_4 [4, 5]

option

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Question no. 11

If the equation a_nxⁿ + a_n-1x^n-1 ...... a₁ x = 0 a₁ ≠ 0, n ≥ 2, has a positive root x = α, then the equation na_nx^n-1 + (n-1)a_n-1x^n-2 + ....... a₁=0 has a positive root, which is (2005)

looks_one greater than α

looks_two smaller than α

looks_3 greater than or equal to α

looks_4 equal to α

option

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Question no. 12

If the roots of the quadratic equation x² + px + q = 0 are tan30° and tan15°, respectively then the value of 2 + q − p is (2006)

looks_one 2

looks_two 0

looks_3 3

looks_4 1

option

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Question no. 13

All the values of m for which both roots of the equations x² − 2mx + m² − 1 = 0 are greater than −2 but less than 4, lie in the interval (2006)

looks_one −2 < m < 0

looks_two m > 3

looks_3 −1 < m < 3

looks_4 1 < m < 4

option

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Question no. 14

If the difference between the roots of the equation x² + ax + 1 = 0 is less than 5 , then the set of possible values of a is (2007)

looks_one (−3, 3)

looks_two (−3, ∞)

looks_3 (3, ∞)

looks_4 (−∞, −3)

option

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Question no. 15

The quadratic equations x² – 6x + a = 0 and x² – cx + 6 = 0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 : 3. Then the common root is (2008)

looks_one 1

looks_two 4

looks_3 3

looks_4 2

option

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Question no. 16

If the roots of the equation bx² + cx + a = 0 be imaginary, then for all real values of x, the expression 3b²x² + 6bcx + 2c² is (2009)

looks_one greater than 4ab

looks_two less than 4ab

looks_3 greater than – 4ab

looks_4 less than – 4ab

option

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