How would you show this?

Questions
,
1

Suppose that x1 and x2 are the roots of the quadratic equation ax^2+bx+c
By writing this in the form

a(x-x1)(x-x2)=0

Show that

x1x2=c/a
x1+x2=-b/a

Hence write down a quadratic equation with roots 3+2i and 1-i,

2

In[6]:= solution = Solve[a x^2 + b x + c == 0, x]

Out[6]= {{x -> (-b - Sqrt[b^2 - 4 a c])/(
   2 a)}, {x -> (-b + Sqrt[b^2 - 4 a c])/(2 a)}}

In[7]:= {x1, x2} = x /. solution

Out[7]= {(-b - Sqrt[b^2 - 4 a c])/(2 a), (-b + Sqrt[b^2 - 4 a c])/(
 2 a)}

In[8]:= x1 x2 // Simplify

Out[8]= c/a

In[9]:= x1 + x2 // Simplify

Out[9]= -(b/a)
3

Thanks David

4

I will point out that this site is not intended for “How do I do my homework problem?” questions.

5

Good point! I should have asked what has been tried… I usually do :wink: