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Definition of Function

Let fx=x4+a x...

Question

Let $f (x) = x^{4} + a x^{3} + b x^{2} + c x + d$ be a polynomial with real co efficient and real roots. Also |f(x)| = 1,then the value of a + b + c+ d is___

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Solution

Conceptual

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= x^{4} + a x^{3} + b x^{2} + c x + d

(2 i) = f (2 + i) = 0

(a + b + c + d)

x^{4} + a x^{3} + b x^{2} + c x + 1 = 0

a, b, c a, b, c

c

f (x) = a x^{3} + b x^{2} + c x - 3

x_{1}, x_{2}, x_{3}, (x_{i} > 0)

f (x) = 0

3 \sum i, j, k = 1 i \neq j \neq k \frac{x_{i}}{x_{j} + x_{k}} = \frac{3}{2}

f (x) = x^{4} + a x^{3} + b x^{2} + c x + d,

a, b, c, d \in Q .

f (\sqrt{3}) = f (3 + i) = 0,

a + b + c + d

f (x) = a x^{3} + b x^{2} + c x - 3

x_{1}, x_{2}, x_{3}, (x_{i} > 0)

f (x) = 0

3 \sum i, j, k = 1 i \neq j \neq k \frac{x_{i}}{x_{j} + x_{k}} = \frac{3}{2}

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