Let f(x)=x^4+a x^3+b x^2+c be a polynomial with real coefficients such that f(1)=-9. Suppose that i \sqrt{3} is a root of the equation 4 x^3+3 a x^2+2 b x=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 ________. [JEE Adv 2024 P1]

JEE Advanced 2024 Paper 1

Section: Mathematics

Question : 9 of 51

Marks: +1, -0

Let f(x)=x4+ax3+bx2+c be a polynomial with real coefficients such that f(1)=−9. Suppose that i√3 is a root of the equation 4x3+3ax2+2bx=0, where i=√−1. If α1,α2,α3, and α4 are all the roots of the equation f(x)=0,then |α1|2+|α2|2+|α3|2+|α4|2 is equal to ________.

[JEE Adv 2024 P1]

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