Respuesta :

use quadratic formula
if you had ax^2+bx+c=0, then
x=[tex] \frac{-b+/- \sqrt{b^{2}-4ac} }{2a} [/tex]
a=1
b=?
c=34
subsitute
[tex] \frac{-b+/- \sqrt{b^{2}-4(1)(34)} }{2(1)} [/tex]=5+/-3i
[tex] \frac{-b+/- \sqrt{b^{2}-136} }{2} [/tex]=5+/-3i
make 5+/-3 into fraction over 2,(10+/-6i)/2
[tex] \frac{-b+/- \sqrt{b^{2}-136} }{2} [/tex]=(10+/-6i)/2
multiply both sides by 2
[tex]-b+/- \sqrt{b^{2}-136} [/tex]=10+/-6i
we conclude that -b=10
b=-10

ok so equaton is
x^2-10x+34


The roots of  x² -bx+34=0  are 5 ± 3i.  Then b = ?

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Vieta's formulas :

5 - 3i + 5 + 3i = b ⇒ b =10 

Now, we have the equation:

x² -10x + 34 = 0