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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`
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