Question

the roots of the quadratic equation z^2 + az + b = 0 are 2 - 3i and 2 + 3i. What is a+b?

Answer 1

ok... so if you use the roots, you should know

\[x = 2 \pm \sqrt{-9}\]

so this becomes

\[x - 2 = \sqrt{-9}\]

so you should be able to get the original quadratic from here

Answer 2

but how do you get a b? im sorry im confused

Answer 3

@campbell_st

Answer 4

ok... let's just work on getting the factored quadratic

so is you square both sides you get

\[(z^2 -2)^2 = -9\]

or

\[z^2 - 4z + 4 = -9\]

Answer 5

so add 9 to both sides and compare it to the original to find a and b

then you can find a + b

Answer 6

z^2-4x+13=0?

Answer 7

great so a=? and b = ?

then find a + b

Answer 8

4 and 13

Answer 9

almost.. check the sign for a...

Answer 10

so 17 is a+b?

Answer 11

well just check

\[z^2 + az + b = 0\]

\[z^2 - 4z + 13 = 0\]

Answer 12

wait so is it -4

Answer 13

correct

Answer 14

so total is 9

Answer 15

correct

Answer 16

thanks

Answer 17

\[ax^2+bx+c=0\]
\[\sum~of~roots=-\frac{ b }{ a }\]
product of roots=c/a