If z= x +iy is a complex numbe

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 Multiple Choice QuestionsMultiple Choice Questions

191.

The biquadratic equation, two of whose roots are 1 + i, 1 - 2, is

  • x4 - 4x3 + 5x2 - 2x - 2 = 0

  • x4 + 4x3 - 5x2 + 2x + 2 = 0

  • x4 + 4x3 - 5x2 + 2x - 2 = 0

  • x4 + 4x3 + 5x2 - 2x + 2 = 0


192.

If the equations x2 + ax + b = 0 and x2 + bx + a = 0(a ± b) have a common root, then a + b is equal to

  • - 1

  • 1

  • 3

  • 4


193.

If 3 is a root of x2 + kx - 24 = 0. It is also a root of

  • x2 + 5x + k = 0

  • x2 + kx + 24 = 0

  • x2 - kx + 6 = 0

  • x2 - 5x + k = 0


194.

To remove the second term of the equation x4 - 8x3 + x2 - x + 3 = 0, diminish the roots of the equation by

  • 1

  • 2

  • 3

  • 4


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195.

The maximum possible number of real roots of the equation x5 - 6x2 - 4x + 5 = 0 is

  • 0

  • 3

  • 4

  • 5


196.

If α, β, γ are the roots of the equation x3 + ax2 + bx + c = 0,then α - 1β -1γ -1 is equal to

  • ac

  • ca

  • bc

  • None of these


197.

If 1 + 3i2 is a root of the equation x4 - x2 + x - 1 = 0.Then, its real roots are

  • 1, 1

  • - 1, - 1

  • 1, 2

  • 1, - 1


198.

If α, β, γ are the roots of 2x3 - 2x - 1 = 0, then αβ2 is equal to

  • - 1

  • 1

  • 2

  • 3


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199.

If z= x +iy is a complex number satisfying z + i22 = z - i22, then the locus of z is

  • x-axis

  • y-axis

  • y = x

  • 2y = x


A.

x-axis

We have,z + i22 = z - i22 x + iy + i22 = x + iy - i22 x + iy + 122 = x + iy - 122 x2 + y + 122 = x2 + y - 12 x2 + y2 +14 + y = x2 + y2 +14 - y                           2y = 0                            y = 0Locus of z is x-axis.


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200.

If 1 - i is a root of the equation x2 + 9x + b = 0, then b is equal to

  • 1

  • - 1

  • - 2

  • 2


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