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If the equation z^4 + a1z^3 + a2z^2 + a3z + a4 = 0,

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If the equation z4 + a1z3 + a2z2 + a3z + a4 = 0,where a1, a2, a3, a4 are real coefficients different from zero has a pure imaginary root then the expression a3 / a1 a2 + a1 a4/a2a3 has the value equal to 

(A) 0 

(B) 1 

(C) – 2 

(D) 2 

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1 Answer

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Best answer

Correct option is (B)

Explanation:

Z4 + a1Z3  + a2Z2 + a3Z + a4 =0

b4 – ib3a1 – b2a2 + iba3 + a4 = 0 

b4 – b2a2 + a4 = 0 ⇒ b4a2 + a4a2 = b2a22

⇒ ba3 – b3a1 = 0 ⇒ a3 = b2a1

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