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
`(c )` Let `f(x)=(x-x_(1))(x-x_(2))(x-x_(3))(x-x_(4))`
`implies|f(i)|=sqrt(1+x_(1)^(2))sqrt(1+x_(2)^(2))sqrt(1+x_(3)^(2))sqrt(1+x_(4)^(2))=1`
`impliesx_(1)=x_(2)=x_(3)=x_(4)=0`
`implies` All four roots are zero.
`implies f(x)=x^(4)impliesa+b+c+d=0`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Comprehension|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE|Exercise Multiple Correct Answer|6 Videos

  • STRAIGHT LINES

    CENGAGE|Exercise JEE Advanced Previous Year|4 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE|Exercise Question Bank|12 Videos

Similar Questions

Explore conceptually related problems

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

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

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

Column I: Equation, Column II: No. of roots x^2tanx=1,x in [0,2pi] , p. 5 2^(cosx)=|sinx|,x in [0,2pi] , q. 2 If f(x) is a polynomial of degree 5 with real coefficients such that f(|x|)=0 has 8 real roots, then the number of roots of f(x)=0. , r. 3 7^(|x|)(|5-|x||)=1 , s. 4

Find the monic polynomial equation of minimum degree with real coefficients given that sqrt3+i is a root.

f(x) is polynomial of degree 4 with real coefficients such that f(x)=0 satisfied by x=1, 2, 3 only then f'(1) f'(2) f'(3) is equal to -

Find the monic polynomial equation of minimum degree with real coefficients having 2-sqrt(3)i as a root.

Let f(x) be a polynomial of degree 5 such that f(|x|)=0 has 8 real distinct , Then number of real roots of f(x)=0 is ________.

Let f(x) be continuous functions f: RvecR satisfying f(0)=1a n df(2x)-f(x)=xdot Then the value of f(3) is 2 b. 3 c. 4 d. 5