Complex Numbers And Quadratic Equations question 9
Question: $ x^{2}-11x+a $ and $ x^{2}-14x+2a $ will have a common factor, if $ a= $ [Roorkee 1981]
Options:
A) 24
B) 0, 24
C) 3, 24
D) 0, 3
Show Answer
Answer:
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 $ {{( \frac{a}{3} )}^{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.
BETA
