- #1

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s^2 + 6s + 25

i know the answer is (s +3 - i4)(s +3 - j4)

but how do i get that?

- Thread starter ACLerok
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- #1

- 194

- 0

s^2 + 6s + 25

i know the answer is (s +3 - i4)(s +3 - j4)

but how do i get that?

- #2

lurflurf

Homework Helper

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You could use the quadratic formula.ACLerok said:

s^2 + 6s + 25

i know the answer is (s +3 - i4)(s +3 - j4)

but how do i get that?

- #3

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Edit: no doubt dexter or someone will tell me this is wrong .

- #4

George Jones

Staff Emeritus

Science Advisor

Gold Member

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Set your expression equal to zero and the roots, i.e. find s = a and s = b such thatACLerok said:

s^2 + 6s + 25

i know the answer is (s +3 - i4)(s +3 - j4)

but how do i get that?

0 = s^2 +6s +25.

Then,

0 = s^2 +6s +25

= (s - a)(s - b).

You could use the quadratic formula, but I think completing the square offers more insight.

Write

0 = s^ + 6s + c^2 - c^2 +25.

Now find c such that

s^ + 6s +c^2 = (s + c)^2.

This means that 2c = 6 and c = 3. Therefore,

0 = s^2 + 6s + 9 - 9 +25

= (s+3)^2 +16

So,

(s + 3)^2 = -16.

Regards,

George

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