• # question_answer 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] A) 3B) 1C) - 2D) 2

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  $1+a-3=0\Rightarrow a=2.$
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