Answer:
If we consider a general quadratic equation:
ax2+bx+c=0
And suppose that we denote roots by α and β, then
x=α,β⇒(x−α)(x−β)=0
∴x2−(α+β)x+αβ=0
Equivalently we can write as
∴x2−(sum of roots)x+(product of roots)=0
And comparing these identical equations we can readily derive the following important relationships:
sum of roots=−ba and product of roots=ca
We also know that complex roots appear in conjugate pairs, so we can form some suitable equations.
Ex 1: α,β=1±2i
S=(1−2i)+(1+2i)=2
P=(1−2i)(1+2i)=1+4=5
So the equation with these roots is:
x2−2x+5=0
Ex 2: α,β=2±1i
S=(2−i)+
Step-by-step explanation:
Hope this helps!!
