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Question
If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e is ______.
Options
0
–2
3
–1
MCQ
Fill in the Blanks
Solution
If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e is 0.
Explanation:
ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`
Put x = 0 both sides
e = `|(0, -1, 1),(1, 0, -1),(-1, 1, 0)|` = 0 ...(Skew symmetric)
∴ e = 0
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