Question

If $\left|\begin{array}{ccc}1& a& a^2\\ 1& x& x^2\\ b^2& ab& a^2\end{array}\right|=0$ then, $x=$

• A. a
• B. $b$
• C. $\frac{a}{b},a$
• D. $\frac{b}{a},a$
• E. 0

Answer 1

Answer: (C)

$\left|\begin{array}{ccc}1& a& a^2\\ 1& x& x^2\\ b^2& ab& a^2\end{array}\right|$
Applying, $R_3\to R_3-R_1$ and $R_2\to R_2-R_1$
We get,
$(x-a)(b-1)\left|\begin{array}{ccc}1& a& a^2\\ 0& 1& x+a\\ b+1& a& 0\end{array}\right|=0$
Which gives $x=\frac{a}{b},a$