Question

If z₁ , z₂ ,z₃ , z₄ are roots of the equation a₀z⁴ + a₁z³ + a₂z² + a₃z + a₄ = 0, where a₀ , a₁ , a₂ , a₃ and a₄ are real, then

(A)  bar (z₁ , z₂ , z₃ , z₄ are also roots of the equation 

(B)  z₁ is equal to at least one of  bar (z₂,  z₃ , z₄) 

(C)  bar(-z₁ , -z₂ ,- z₃ , z₄) are also roots of the equation

(D) None of the above.

Answer 1

Correct option (A)(B)

Explanation:

are the roots of the equation if z₁ is real, then  bar z₁ is also real and if  bar z₁ is non real, then 1 z is also root because imaginary roots occur in conjugate pair.