Home
Class 12
MATHS
Let f(x) = x^4 + ax^3 + bx^2 + cx + d be...

Let` f(x) = x^4 + ax^3 + bx^2 + cx + d` be a polynomial with real coefficients and real roots. If |f(i)|=1where `i=sqrt(-1)`, then the value of a +b+c+d is

A

`-1`

B

1

C

0

D

can't be determined

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|22 Videos
  • COMPLEX NUMBER

    FIITJEE|Exercise COMPREHENSION - I|3 Videos
  • COMPLEX NUMBER

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|10 Videos
  • CIRCLE

    FIITJEE|Exercise Numerical Based|2 Videos
  • DEFINITE INTEGRAL

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=x^(3)+ax^(2)+bx+c be a cubic polynomial with real coefficients and all real roots.Also |f(iota|=1 where iota=sqrt(-1) statement-1: All 3roots of f(x)=0 are zero Statement-2: a+b+c=0

Let f(x)=ax^(3)+bx^(2)+cx+d be a cubic polynomial with real coefficients satisfying f(i)=0 and f(1+i)=5. Find the value of a^(2)+b^(2)+c^(2)+d^(2)

Let P(x)=x^(3)-8x^(2)+cx-d be a polynomial with real coefficients and with all it roots being distinct positive integers.Then number of possible value of c is

A nonzero polynomial with real coefficient has the property that f(x)=f'(x)f(x) .If a is the leading coefficient of f(x), then the value of (1)/(2a) is

Let f (x) =x ^(2) + ax +b and g (x) =x ^(2) +cx+d be two quadratic polynomials with real coefficients and satisfy ac =2 (b+d). Then which of the following is (are) correct ?

Let P(x)=x^3+ax^2+bx+c be a polynomial with real coefficients, c!=0andx_1,x_2,x_3 be the roots of P(x) . Determine the polynomial Q(x) whose roots are 1/x_1,1/x_2,1/x_3 .

The polynomial f(x)=x^(4)+ax^(3)+bx^(3)+cx+d has real coefficients and f(2i)=f(2+i)=0. Find the value of (a+b+c+d)

Let f(x) be a polynomial with real coefficients such that f(0)=1 and for all x ,f(x)f(2x^(2))=f(2x^(3)+x) The number of real roots of f(x) is:

FIITJEE-COMPLEX NUMBER-ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I
  1. If z= 5e^(itheta), then |e^(iz)| is equal to

    Text Solution

    |

  2. The complex number satisfying |z+bar(z)|+|z - bar(z)|=2 and |z+i|+|z-i...

    Text Solution

    |

  3. Let f(x) = x^4 + ax^3 + bx^2 + cx + d be a polynomial with real coeffi...

    Text Solution

    |

  4. If z1 and z2 are two complex numbers, then the equation of the perpend...

    Text Solution

    |

  5. If z= x+iy satisfies the equation arg (z-2)="arg" (2z+3i), then 3x-4y ...

    Text Solution

    |

  6. If alpha = x + y + z + omega and beta = (xy + yz + zomega + omega x + ...

    Text Solution

    |

  7. If P and Q are represented by the complex numbers z1 and z2 such that...

    Text Solution

    |

  8. The complex number sin(x)+icos(2x) and cos(x)-isin(2x) are conjugate t...

    Text Solution

    |

  9. For any complex number z, maximum value of |z|-|z-1| is

    Text Solution

    |

  10. If infty(a(1)+ib(1))(a(2)+ib(2))………………(a(n)+ib(n))=A+iB, then sum(i=1)...

    Text Solution

    |

  11. The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1...

    Text Solution

    |

  12. If z= x+iy , z^(1//3) = a- ib and (x)/(a) - (y)/(b) = lambda (a^(y) -...

    Text Solution

    |

  13. If z= (1)/(2) (sqrt3 -i), then the least positive integral value of ...

    Text Solution

    |

  14. The value of the expression 2(1+(1)/(omega))(1+(1)/(omega^(2)))+3(2+(1...

    Text Solution

    |

  15. If w = alpha+ibeta, where beta ne 0 and z ne 1, satisfies the condit...

    Text Solution

    |

  16. If |z-i| lt 1, then the value of |z + 12-6i| is less than

    Text Solution

    |

  17. If a, b, c are integers not all equal and w is a cube root of unity (w...

    Text Solution

    |

  18. If theta(i) in [ 0, pi//6], I = 1, 2, 3, 4, 5 and sin theta(i)z^(4) ...

    Text Solution

    |

  19. If |z-2|= "min" {|z-1|,|z-3|}, where z is a complex number, then

    Text Solution

    |

  20. If a complex number z satisfies log(1//sqrt2) ((|z|^2 + 2 |z|+6)/(2 |z...

    Text Solution

    |