Determine the sum of imaginary roots of the equation (2x + x - 1)

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 Multiple Choice QuestionsMultiple Choice Questions

91.

If logex2 - 16  loge4x - 11, then

  • 4 < x  5

  • x < - 4 or x > 4

  • - 1 < x  5

  • x < - 1 or x > 5


 Multiple Choice QuestionsShort Answer Type

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92.

Determine the sum of imaginary roots of the equation (2x + x - 1) ( 4x2 + 2x - 3) = 6


Given, (2x + x - 1) ( 4x2 + 2x - 3) = 6

Put 2x2 + x = y

 y - 12y - 3 = 6   2y2 - 5y - 3 = 0                       y = 3, - 12     2x2 + x - 3 = 0                 2x2 +x = - 12  4x2 + 2x + 1 = 0

Discriminants,

D1 = 1 + 4 x 3 = 13 > 0, real roots

D2 = 4 - 16 = - 12 < 0, imaginary roots

 Sum of roots of 4x + 2x + 1 = 0 is

α + β = - 24 = - 12


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 Multiple Choice QuestionsMultiple Choice Questions

93.

Let a, b, c be three real numbers, such that a + 2b + 4c = 0, Then, the equation ax2 + bx + c = 0

  • has both the roots complex

  • has its roots lying within - 1 < x < 0

  • has one of roots equal to 12

  • has its roots lying within 2 < x < 6


94.

If the ratio of the roots of the equation px+ qx + r = 0 is a : b, then aba + b2

  • p2qr

  • prq2

  • q2pr

  • pqr2


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95.

If α and β  are the roots of the equation x2 + x + 1 = 0, then the equation whose roots are α19 and β7 is

  • x2 - x - 1 = 0

  • x2 - x + 1 = 0

  • x2 + x - 1 = 0

  • x2 + x + 1 = 0


96.

For the real parameter t, the locus of the complex number z = 1 - t2 + i1 + t2 in the complex plane is

  • an ellipse

  • a parabola

  • a circle

  • a hyperbola


97.

If α, β be the roots of the quadratic equation x2 + x + 1 = 0, then the equation whose roots are α19. β7 f is

  • x2 - x + 1 = 0

  • x2 - x - 1 = 0

  • x2 + x - 1 = 0

  • x2 + x + 1 = 0


98.

The roots of the quadratic equation x2 - 23x - 22 = 0 are

  • imaginary

  • real, rational and equal

  • real, irrational and unequal

  • real, rational and unequal


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99.

The quadratic equation x2 + 15x + 14 = 0 has

  • only positive solutions

  • only negative solutions

  • no solution

  • both positive and negative solution


100.

If z = 41 - i, then z¯ is (where z¯ is complex conjugate of z)

  • 2(1 + i)

  • (1 + i)

  • 21 - i

  • 41 + i


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