Question

The three roots of the equation $\left| \begin{array} { l l l } \mathrm { x } & 3 & 7 \\ 2 & x & 2 \\ 7 & 6 & x \end{array} \right|$ = 0 are

• A. 9, 2, – 7
• B. – 9, 2, 7
• C. 9, –2, 7
• D. None of these

Answer 1

Answer: (B)

– 9, 2, 7

Answer 2

R₁ + R₂ + R₃ & taking

Common (x + 9)

∆ = (x + 9) $\left| \begin{matrix} 1 & 1 & 1 \\ 2 & x & 2 \\ 7 & 6 & x \end{matrix} \right|$

C₂ → C₂ – C₁, C₃ → C₃ – C₁

∆ = (x + 9) $\left| \begin{matrix} 1 & 0 & 0 \\ 2 & x–2 & 0 \\ 7 & –1 & x–7 \end{matrix} \right|$

∆ = (x + 9) (x – 2) (x – 7) = 0

∆ = – 9, 2, 7