Question

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

Answer 1

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

Answer 2

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