Question
Question: If f(x) = x<sup>4</sup> + ax<sup>3</sup> + bx<sup>2</sup> + cx + d be polynomial with real coefficie...
If f(x) = x4 + ax3 + bx2 + cx + d be polynomial with real coefficient and real roots. If |f(i)| = 1, i = −1 , then
a + b + c + d is equal to
A
– 1
B
1
C
0
D
Cann't be determined
Answer
0
Explanation
Solution
Let f(x) = (x – x1)(x – x2)(x – x3)(x – x4)
Q | f (i)| = 1+x121+x221+x321+x42= 1
⇒ x1 = x2 = x3 = x4 = 0
⇒ All four roots are zero ⇒ f(x) = x4
∴ a = b = c = d = 0
⇒ a + b + c + d = 0