Solveeit Logo

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\sqrt{- 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\sqrt{1 + {x_{1}}^{2}}\sqrt{1 + {x_{2}}^{2}}\sqrt{1 + {x_{3}}^{2}}\sqrt{1 + {x_{4}}^{2}}= 1

⇒ x1 = x2 = x3 = x4 ­= 0

⇒ All four roots are zero ⇒ f(x) = x4

∴ a = b = c = d = 0

⇒ a + b + c + d = 0