Question

find the zeros of this function:
g(x)= x^2 + 6x + 34

Answer 1

to get zeros of g(x), equate g(x) = 0
and you get a quadratic equation of the form ax^2+bx+c=0
Compare your quadratic equation with \(ax^2+bx+c=0\)
find \[a=...?\\b=...?\\c=...?\]
then the two roots of x are:
\(\huge{x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)

Answer 2

a= x
b= 6
c= 34

Answer 3

a=1
b= 6, c=34 is correct :)

Answer 4

what do i do after that?

Answer 5

calculate \(b^2-4ac=... ?\)

Answer 6

i got -100..

Answer 7

b^2-4ac = 36 - 4*34 = -100 is correct, so,
\(\sqrt {b^2-4ac}= \sqrt{-100} =10i\)
just substitute this in the quadratic formula above.

Answer 8

what do i substitute?

Answer 9

\(\huge{x_{1,2}=\frac{-b \pm \sqrt{b^2-4ac}}{2a}}\)
just plug in values!
yo know a,b, and b^2-4ac..

Answer 10

i put all the values in but i cant solve it because i dont have my calculator

Answer 11

You don't need a calculator for this!

Answer 12

you don't need calc
b=6, a=1
\(\huge{x_{1,2}=\frac{-6 \pm 10i}{2}}\)

Answer 13

That can be simplified to
\[-3\pm5i\]

Answer 14

in the back of my book it says the answer is -3 (plus minus} 5i

Answer 15

ahh okay thank you

Answer 16

-6/2 = -3
10i/2 = 5i
-10i/2 = -5i

Answer 17

now since youre all here, how do you express each number in terms of i for
1/2 (squareroot) -16

Answer 18

and (squareroot) -144

Answer 19

note \(\sqrt{-n}= \sqrt{-1}\sqrt {n}= i \sqrt n\)

Answer 20

remember that i^2 = -1
so \[\sqrt{-144} = \sqrt{-1*144}=i\sqrt{144}\]

Answer 21

whpalmer4 : so what do i do after that?

Answer 22

What is the square root of 144? Factor it:

144= 2*72 = 2*2*36 = 2*2*2*18 = 2*2*2*2*9=2*2*2*2*3*3

For every pair of identical factors, move one of them outside of the square root sign.
\[\sqrt{144}=\sqrt{(2*2)*(2*2)*(3*3)}=2*2*3=12\]

Answer 23

So \[\sqrt{-144}=i\sqrt{144}=12i\]

Answer 24

yes i got that. what about1/2 \[\sqrt{-16}\]

Answer 25

\[1/2\sqrt{-16}\]

Answer 26

can't you find square root of 16 ?

Answer 27

i got 2i

Answer 28

yes, square root of 16 = 4 and (1/2) 4 = 2
and don't forget to have negative root,
+2i and -2i

Answer 29

okay thanks

Answer 30

welcome ^_^