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If 3-2i and 1+i are two of the roots of the eq

z⁴+az³ + bz² +cz +d =0

Find values of a,b,c and d

1 Answer

5 votes

Answer:

steps below

Explanation:

will solve a and d here, to solve c and d is crazy.

for this equation we have 4 roots: p (3-2i), q(3+2i), r(1+i), s(1-i)

z⁴+az³ + bz² +cz +d = (z+p)(z+q)(z+r)(z+s) = 0

= z⁴ + (p+q+r+s)z³ + (pq+pr+ps+qr+qs+rs)z²

+(pqr+pqs+prs+qrs)z + pqrs

d = pqrs = (3-2i)(3+2i)(1+i)(1-i) = (9-4(-1))(1-1(-1) = 13*2 = 26

a = p+q+r+s = (3-2i)+(3+2i)+(1+i)+(1-i) = 8

b = pq+pr+ps+qr+qs+rs .... calculate it , if you are interested

c = pqr+pqs+prs+qrs

User Aram Paronikyan
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