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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    CENGAGE ENGLISH|Exercise All Questions|365 Videos
  • CONIC SECTIONS

    CENGAGE ENGLISH|Exercise All Questions|1344 Videos

Similar Questions

Explore conceptually related problems

The quadratic equation ax^(2)+bx+c=0 has real roots if:

If the quadratic equation alpha x^2 +beta x+a^2+b^2+c^2-ab-bc-ca=0 has imaginary roots then

Consider a quadratic equation az^2 + bz + c =0 where a, b, c, are complex numbers. Find the condition that the equation has (i) one purely imaginary root (ii) one purely real root (iii) two purely imaginary roots (iv) two purely real roots

If f(x)=x has non real roots, then the equation f(f(x))=x (A) has all real and unequal roots (B) has some real and non real roots (C) has all real and equal roots (D) has all non real roots

Find the real number x if (x−2i)(1+i) is purely imaginary.

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

The equation ax^(2)+6x-9=0 will have imaginary roots if

Show that the equation x^2+a x-4=0 has real and distinct roots for all real values of a .

If p,q,r epsilon R and are distinct the equation (x-p)^5+(x-q)^5+(x-r)^5=0 has (A) four imaginary and one real root (B) two imaginary and three real roots (C) all the roots real (D) none of these

If z is a unimodular number (!=+-i) then (z+i)/(z-i) is (A) purely real (B) purely imaginary (C) an imaginary number which is not purely imaginary (D) both purely real and purely imaginary

CENGAGE ENGLISH-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 and beta be the roots x^2-6x-2=0, with alpha > beta If an=al...

    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. Minimum value of| z1- z2| as z1& z2 over the curves √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 at least one of them is great...

    Text Solution

    |

  14. If |z-1|-1,t h e n a r g((z-1-i)//z) can be equal to pi//4 (z-2)//z ...

    Text Solution

    |

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

    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. Column I, Column II (Locus) parallelogram, p. z1-z4=z2-z3 rectang...

    Text Solution

    |