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Find a cubic polynomial with real coefficients having roots x = 5 and x = -3i. Assume a lead coefficient of 1.

2007-10-26 06:24:53 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

P(x) = (x-5)(x^2+9)

2007-10-26 06:30:53 · answer #1 · answered by santmann2002 7 · 0 0

a cubic poly :
(x-5)*(x+3*i)*(x-a)
(x^2+(3*i-5)*x-15i)*(x-a)
x^3+(3*i-5)*x^2-15*i*x-a*x^2-(3i-5)*a*x-15*i*a
x^3 + [ 3*i-5-a]*x^2 + [ -15*i-(3*i-5)*a]*x-15*i*a

so
3*i-5-a must be real
so
a= 3*i

so
the cubic poly is :
(x-5)*(x-3*i)(x+3*i)
or
(x-5)*(x^2+9)

2007-10-26 13:39:14 · answer #2 · answered by buz 4 · 0 0

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