Home
Class 11
MATHS
The quadratic equation p(x)=0 with real...

The quadratic equation `p(x)=0` with real coefficients has purely imaginary roots. Then the equation `p(p(x))=0` has A. only purely imaginary roots B. all real roots C. two real and purely imaginary roots D. neither real nor purely imaginary roots

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise All Questions|363 Videos

  • CONIC SECTIONS

    CENGAGE PUBLICATION|Exercise All Questions|1167 Videos

Similar Questions

Explore conceptually related problems

The quadratic equations p(x) =0 with real coefficients has purely imaginary roots. Then the equation p(p(x))=0 has

The real roots of the equation

Find the quadratic equation with real coefficients which has 2+i as a root (i=sqrt-1) .

Find the quadratic equation with real coefficients which has 2±3i as a root (i=sqrt-1)

The quadratic equation x^(2)-2x+1=0 have no real root.

Given z is a complex number with modulus 1. Then the equation [(1+i a)/(1-i a)]^4=z has all roots real and distinct two real and two imaginary three roots two imaginary one root real and three imaginary

If a, b , c in R and 3b^(2)-8ac lt 0 , then the equation ax^(4)+bx^(3)+cx^(2)+5x-7=0 has a) all real roots b) all imaginary roots c)exactly two real and two imaginary roots d) none

If b_1. b_2=2(c_1+c_2) then at least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has a) imaginary roots b) real roots c) purely imaginary roots d) none of these

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

CENGAGE PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-All Questions
  1. For real x, the function ((x-a)(x-b))/(x-c) will assume all real value...

    Text Solution

    |

  2. If z1, z2 are two complex numbers (z1!=z2) satisfying |z1^2-z2^2|=| z...

    Text Solution

    |

  3. The quadratic equation p(x)=0 with real coefficients has purely imagi...

    Text Solution

    |

  4. If from a point P representing the complex number z1 on the curve |z...

    Text Solution

    |

  5. Let alpha, beta be the roots of the equation x^(2)-6x-2=0 with alpha g...

    Text Solution

    |

  6. If |z-3|=min{|z-1|,|z-5|}, then Re(z) equals to

    Text Solution

    |

  7. For the following question, choose the correct answer from the codes ...

    Text Solution

    |

  8. Find the value of 1^3

    Text Solution

    |

  9. All the values of m for whilch both the roots of the equation x^2-2m x...

    Text Solution

    |

  10. If p=a+bomega+comega^2, q=b+comega+aomega^2, and r=c+aomega+bomega^2,...

    Text Solution

    |

  11. If the roots of the quadratic equation (4p-p^2-5)x^2-(2p-1)x+3p=0 lie ...

    Text Solution

    |

  12. If z1=5+12 i and |z2|=4,t h e n

    Text Solution

    |

  13. If roots of x^2-(a-3)x+a=0 are such that both of them is greater than ...

    Text Solution

    |

  14. If (z-1)/(z+1) is purely imaginary then

    Text Solution

    |

  15. Let f(x)=a x^2+bx +c a ,b ,c in R. If f(x) takes real values for...

    Text Solution

    |

  16. Write a linear equation representing a line which is parallel to y-axi...

    Text Solution

    |

  17. If both roots of the equation a x^2+x+c-a=0 are imaginary and c > -1, ...

    Text Solution

    |

  18. If |z|=1 and w=(z-1)/(z+1) (where z!=-1), then R e(w) is 0 (b) 1/(|...

    Text Solution

    |

  19. The set of all possible real values of a such that the inequality (x-(...

    Text Solution

    |

  20. If z1, z2 are complex number such that (2z1)/(3z2) is purely imaginary...

    Text Solution

    |