Question

The roots of x2 − ( ) + 34 are 5 ± 3i.

Answer 1

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

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

Answer 2

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