Home
Class 12
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 only purely imaginary roots at real roots two real and purely imaginary roots neither real nor purely imaginary roots

A

only purely imaginary roots

B

all real roots

C

two real and two purely imaginary roots

D

neither real nor purely imaginary roots

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Main ( Archive ) (Fill in the blanks )|3 Videos
  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise JEE Advance ( Archive )|20 Videos
  • QUADRATIC EQUATIONS & INEQUATIONS

    VMC MODULES ENGLISH|Exercise Numerical value type of JEE Main|15 Videos
  • PROPERTIES OF TRIANGLE

    VMC MODULES ENGLISH|Exercise JEE Advanced (Archive)|50 Videos
  • QUIZ

    VMC MODULES ENGLISH|Exercise MATHEMATICS|30 Videos

Similar Questions

Explore conceptually related problems

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

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

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

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

The equation x(x+2)(x ^2 −x)=−1 , has all roots imaginary ,neagative,two real two imaginary or all roots real.

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 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

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

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

VMC MODULES ENGLISH-QUADRATIC EQUATIONS & INEQUATIONS -JEE Main ( Archive )
  1. Let alpha and beta be the roots of the equation x^2-6x-2=0 If an=alpha...

    Text Solution

    |

  2. The quadratic equation p(x)=0 with real coefficients has purely imagin...

    Text Solution

    |

  3. The set of all real numbers x for which x^2-|x+2|+x >0 is (-oo,-2) b. ...

    Text Solution

    |

  4. The number of solution of log4(x-1)=log2(x-3) is :

    Text Solution

    |

  5. For the equation 3x^2+p x+3=0,p >0, if one of the root is square of th...

    Text Solution

    |

  6. The equation sqrt((x+1))-sqrt((x-1))=sqrt((4x-1)) has

    Text Solution

    |

  7. The equation x^((3)/4 (log2x)^2+log2 x -(5)/(4))=sqrt(2) has :

    Text Solution

    |

  8. The equation x-2//x-1=1-2//x-1 has a. no root b. one root c. two equal...

    Text Solution

    |

  9. For real x , the function (x-a)(x-b)//(x-c) will assume all real value...

    Text Solution

    |

  10. The number of real solutions of the equation |x^(2)|-3|x|+2=0 is (a) 3...

    Text Solution

    |

  11. If x lt 0 , lt 0 , x + y +(x)/4=(1)/(2) and (x+y)((x)/y)=-(1)/(2) th...

    Text Solution

    |

  12. Let a gt 0, b gt 0 and c lt0. Then, both the roots of the equation ax^...

    Text Solution

    |

  13. Find the set of all solutions of the equation 2^|y| -|2^(y -1) -1| = 2...

    Text Solution

    |

  14. Find the set of all s for which (2x)/(2x^(2)+5x+2) gt (1)/(x+10

    Text Solution

    |

  15. Solve for x :(5+2sqrt(6))^(x^2-3)+(5-2sqrt(6))^(x^2-3)=10.

    Text Solution

    |

  16. The number of solution (s) for the equation 2logxa+log(ax)a+3log(a^2x)...

    Text Solution

    |

  17. A value of b for which the equation x^2+b x-1=0,x^2+x+b=0 have one roo...

    Text Solution

    |

  18. For all ' x^(prime),x^2+2a x+(10-3a)>0, then the interval in which ' a...

    Text Solution

    |

  19. If the roots of the equation x^2-2a x+a^2-a-3=0 are real and less than...

    Text Solution

    |

  20. Find all real values of x which satisfy x^2-3x+2>0a n dx^2-2x-4lt=0.

    Text Solution

    |