Question

Answer the following question:

Find the value of x if

`|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0

Answer 1

`|(1, 4, 20),(1, -2, -5),(1, 2x, 5x^2)|` = 0

∴ 1(–10x² + 10x) – 4(5x² + 5) + 20(2x + 2) = 0

∴  –10x² + 10x – 20x² – 20 + 40x + 40 = 0

∴ – 30x² + 50x + 20 = 0

∴ 3x² – 5x – 2 = 0  ...[Dividing throughtout by (–10)]

∴ 3x² – 6x + x – 2 = 0

∴ 3x(x – 2) + 1(x – 2) = 0

∴ (x – 2) (3x + 1) = 0

∴ x – 2 = 0 or 3x + 1 = 0

∴ x = 2 or  x = `-1/3`