Complex Numbers And Quadratic Equations question 196
Question: The value of ‘a’ for which the equations $ x^{2}-3x+a=0 $ and $ x^{2}+ax-3=0 $ have a common root is [Pb. CET 1999]
Options:
A) 3
B) 1
C) - 2
D) 2
Show Answer
Answer:
Correct Answer: D
Solution:
Given equations are $ x^{2}-3x+a=0 $ ??(i) and $ x^{2}+ax-3=0 $ ??(ii) Subtracting (ii) from (i), we get
Þ $ -3x-ax+a+3=0 $
$ \Rightarrow (a+3)(-x+1)=0 $
Þ either $ a=-3 $ or $ x=1 $ When $ a=-3, $ the two equations are identical. So, we take $ x=1, $ which is the common root of the two equations. Substituting $ x=1 $ in (i), we get $ 1+a-3=0\Rightarrow a=2. $
BETA
