please help! I will medal and fan! screenshot in comments

Question

anonymous · Answer

attachment

anonymous · Answer

@amistre64

anonymous · Answer

@iGreen @TheSmartOne

anonymous · Answer

@Michele_Laino

amistre64 · Answer

itll help if you review complex roots,  also called imaginary roots.  they have a particularly useful property for us here.

anonymous · Answer

what property? im so confused?

amistre64 · Answer

look in your material, thats the study part of this.  you find something that you think tells you about complex roots, and ill let you know if youve done good or not.

amistre64 · Answer

what do you know about the quadratic formula?

anonymous · Answer

I know the quadratic formula

amistre64 · Answer

given a quadratic equation of the form:

x^2 +2bx + c = 0

the solutions for x can be determined by the formula:  

x = -b +- sqrt(b^2 -c)

we have at best 2 defined roots: 

[-b + sqrt(b^2 -c)]  and 
[-b -  sqrt(b^2 -c)]
     ^^
     these roots differ in their construction by a simple change in sign only

if (n+m) is a root,  then so is (n-m)

anonymous · Answer

$$\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }$$

amistre64 · Answer

good,  your form is more complicated but its the same format nonetheless.

that $\pm$ is the only real difference in the roots.

amistre64 · Answer

so, we have 4 + 17i

whats another root?  change the + to a -

anonymous · Answer

so my answer is 4 - 17i?

amistre64 · Answer

yep

amistre64 · Answer

no, just change the + to a - ... dont add anything else

anonymous · Answer

awesome thank you so much!

amistre64 · Answer

youre welcome

the property that this refers to, is that complex roots come in pairs,  conjugate pairs.

a+b  and  a-b   are called conjugates of each other