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3 and 4 .Determinants and Matrices
normal
The number of real values of $x$ satisfying $\left| {\,\begin{array}{*{20}{c}} x&{3x + 2}&{2x - 1}\\{2x - 1}&{4x}&{3x + 1}\\{7x - 2}&{17x + 6}&{12x - 1}\end{array}\,} \right|$ $= 0$ is
A$3$
B$0$
Cmore than $3$
D$1$
Solution
Use $R_3 \rightarrow R_3 – (2R_2 + 3R_1)$ we get $\left| {\,\begin{array}{*{20}{c}}x&{3x + 2}&{2x – 1}\\{2x – 1}&{4x}&{3x + 1}\\0&0&0\end{array}\,} \right|$ which is equal to zero for all $x$.
Standard 12
Mathematics