quadratic equation whose solutions are.......

[kimmerhc]

I was hoping someone could help me with some of these questions. I really need to see the work involved.

1) Write a quadratic equation whose solutions are 2- i and 2 + i

2) Solve for x: y = the sqare root of 3x-z

I would appreciate any help I can get........

 

[tkhunny]

Given a root, a, there is a factor x-a. That is ALL you need for the first.

Do you really mean "-z"? In any case, square both sides and see if it looks any easier. y >=0 so there is little harm to be done, assuming you have reported the original problem statement.

 

[kimmerhc]

thanks for the quick answer. I will try squaring both sides for the second one.

I don't really understand what you mean when you talk about the first one though. Root 'a'? In my textbook when they have these types of questions the 'solutions' are just a set of numbers, such as (3,2) etc. They show that you figure out the quadratic equation by starting with x = 3, x = 2, and then work from there. I am just unclear as to how to incorporate this formula when my solutions given are 2 - i, and 2 + i.

thanks again.

 

[skeeter]

let a = 2-i
b = 2+i

y = (x-a)(x-b) = x² - (a+b)x + ab

substitute (2-i) for a and (2+i) for b ...

x² - [(2-i)+(2+i)]x + (2-i)(2+i)

combine like terms to find the linear coefficient, multiply to find the constant.

you finish up.