find x

Engineering

Mathematics

Introduction to Determinants

Question

$∣ \begin{array}{ccc} 1 & 4 & 20 \\ 1 & - 2 & 5 \\ 1 & 2 x & 5 x^{2} \end{array} ∣ = 0$ find x

– 1, 2

0, 1

1, 3

2, 0

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$∣ \begin{array}{ccc} 1 & 4 & 20 \\ 1 & - 2 & 5 \\ 1 & 2 x & 5 x^{2} \end{array} ∣ = 0$
r₁ → r₁ – r₂ and r₃ → r₃ – r₂
$∣ \begin{array}{ccc} 0 & 6 & 15 \\ 1 & - 2 & 5 \\ 0 & 2 x + 2 & 5 x^{2} - 5 \end{array} ∣$
= – (6(5x² – 5) – 15(2x + 2))
= – (30² – 30 – 30x – 30)
= 30(– x² + x + 2)
So, x² – x – 2 = 0
x = – 1, 2

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