Consider the following polynomial of x x^2+(a+bg)x+cg^2=0

wasangagac4

wasangagac4

Answered question

2022-10-31

Consider the following polynomial of x
x 2 + ( a + b g ) x + c g 2 = 0
where b R , and c R , whereas g can be complex. c 0

Answer & Explanation

Szulikto

Szulikto

Beginner2022-11-01Added 22 answers

Just like in the real-coefficient case, the roots of a quadratic complex polynomial are given by the quadratic formula. In your case,
x 2 + ( a + b g ) x + c g 2 = ( x + a + b g 2 + a 2 + 2 a b g + ( b 2 4 c ) g 2 2 ) ( x + a + b g 2 a 2 + 2 a b g + ( b 2 4 c ) g 2 2 ) ,
where z is the principal square root.
There is no significantly simpler formulation unless some special relationship exists between a,b,c and g.

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