A quadratic equation with real coefficients and leading coefficient 1 has x=bi as a root. Write in general form

Question

Math 1050. Please show work not just answer

Answer 1

Hi Salt Lake,

 

Ok, so we have a puzzle here.

• I will assume that if I were to give you a quadratic equation, like x² + 3x + 4 = 0, and I asked you for its roots, you could find them?  If not, then we need to back up.  If so, read on...
• In this problem, they've given us one of the roots, and we have to work backwards to figure out the quadratic.

 

So, let's see what we know.

• What's the coefficient in front of the x² equal to, based what they've told us in the problem?
• We know one of the roots is equal to bi. 
• What's the other root?  Hint:  one root is imaginary, but the quadratic has real coefficients.  How did that happen?  Or, another hint:  Find the roots to the quadratic I gave you above, and see what they look like.  If I told you one of those roots, could you have deduced the other one?
• If I know the roots, then how does that help me reconstruct the original quadratic?  Hint:  If I know the roots, then what does that have to do with its factors?  If I knew the factors, then I could multiply them out to get the original quadratic, right?

 

Let us know if that gives you enough of a nudge to figure it out, and if not, I'm sure we can provide a little more help if you can tell us what your questions are...

 

-- Michael