QUADRATIC EQUATIONS - COMMON ROOTS OF TWO QUADRATIC EQUATIONS
QUADRATIC EQUATIONS
a. Only one common root
Let be the common root of
then
By Cramer's Rule
Therefore ,
So the condition for a common root is
b.
If both roots are same then
Example :
Find p and q such that px2 +5x+2=0 and 3x2 +10x+q=0. have both roots in common?
Solution :
a1=p,b1=5,c1=2
a2 = 3, b2 = 10, c2 = q
We know that