Let f(x) = x^4 + ax^3 + bx^2 + c be a polynomial with real coefficients such that f(1) = -9. Suppose that i√(3) is a root of the equation 4x^3 + 3ax^2 + 2bx = 0, where i = √(-1). If α_1, α_2, α_3, and α_4 are all the roots of the equation f(x) = 0, then |α_1|^2 + |α_2|^2 + |α_3|^2 + |α_4|^2 is equal to _______.

Let f(x) = x^4 + ax^3 + bx^2 + c be a polynomial with real… — JEE Advanced 2024 Mathematics PYQ

JEE Advanced 2024 · Paper 1 · numerical answer

Let

f(x) = x^4 + ax^3 + bx^2 + c

be a polynomial with real coefficients such that

f(1) = -9

. Suppose that

i\sqrt{3}

is a root of the equation

4x^3 + 3ax^2 + 2bx = 0

, where

i = \sqrt{-1}

. If

\alpha_1, \alpha_2, \alpha_3

, and

\alpha_4

are all the roots of the equation

f(x) = 0

, then

|\alpha_1|^2 + |\alpha_2|^2 + |\alpha_3|^2 + |\alpha_4|^2

is equal to _______.

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Answer: 20

[JEE Advanced 2024 · Paper 1]

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