The maximum possible number of real roots of the equation x5 

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 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


Advertisement
Advertisement

195.

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

  • 0

  • 3

  • 4

  • 5


B.

3

Let f(x) = x5 - 6x2 - 4x + 5 = 0

  f- x = - x5 - 6x2 + 4x + 5

Number of changes of sign in f(x) are 2 and

number of changes of sign in f(- x) are 1.

 By descarte's rule of signs

Maximum number of +ve real roots are 2 and - ve real roots are 1.

 Maximum possible real roots are 3.


Advertisement
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


Advertisement
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


200.

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

  • 1

  • - 1

  • - 2

  • 2


Advertisement