A) 24
B) 0, 24
C) 3, 24
D) 0, 3
Correct Answer: B
Solution :
Expressions are \[{{x}^{2}}-11x+a\] and\[{{x}^{2}}-14x+2a\]will have a common factor, then \[\Rightarrow \,\,\frac{{{x}^{2}}}{-22a+14a}=\frac{x}{a-2a}=\frac{1}{-14+11}\] Þ \[\frac{{{x}^{2}}}{-8a}=\frac{x}{-a}=\frac{1}{-3}\]Þ \[{{x}^{2}}=\frac{8a}{3}\]and\[x=\frac{a}{3}\] Þ \[{{\left( \frac{a}{3} \right)}^{2}}=\frac{8a}{3}\,\,\,\,\Rightarrow \frac{{{a}^{2}}}{9}=\frac{8a}{3}\]Þ\[a=0,\,\,24\]. Trick: We can check by putting the values of a from the options.
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