First slide

Introduction to Determinants

Question

Let $Δ = |\begin{array}{ccc} 1 & - 4 & 20 \\ 1 & - 2 & 5 \\ 1 & 2 x & 5 x^{2} \end{array}|$ Solution set of $∆ = 0$ is

Moderate

A

${- 2, 3}$
B

${- 3, 4}$
C

${4, - 6}$
D

${- 2, - 1}$

Solution

Applying $R_{2} \to R_{2} - R_{1}, R_{3} \to R_{3} - R_{1}$ we get
$Δ = |\begin{array}{ccc} 1 & - 4 & 20 \\ 0 & 2 & - 15 \\ 0 & 2 (x + 2) & 5 (x^{2} - 4) \end{array}| = 2 (x + 2) |\begin{array}{cc} 1 & - 15 \\ 1 & 5 (x - 2) \end{array}|$
$= 10 (x + 2) (x + 1)$
Now, $Δ = 0 \Rightarrow x = - 2, - 1$

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