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...

Question

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 _1, _2, _3, and _4 are all the roots of the equation f(x) = 0, then | _1|^2 + | _2|^2 + | _3|^2 + | _4|^2 is equal to _____.

Accepted Answer

20

JEE Advanced 2024 Mathematics question

Solution

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