What is the equation of f(x) if (3-5i) and (3+5i) are the roots?
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Let the equation be f(x) = x^2 + bx + c
Then we know that if x1 and x2 are the roots of f(x).
Then x1+x2= -b/a
==> x1*x2= c/a
We have the roots (3-5i) and (3+5i)
==> (3-5i)+(3+5i) = 6 = -b ==> b= -6
==> (3-5i)(3+5i)= 9+25= 34 = c
==> f(x)= x^2 - 6x + 34 = 0
To check we will calculate the roots.
==> x1= (6+sqrt(-100) / 2 = 6+10i / 2 = 3+ 5i
==> x2= 3-5i
Then the equation is: f(x) = x^2 -6x + 34
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