Question

If x = –4 is a root of `|(x, 2, 3),(1, x, 1),(3, 2, x)| = 0`, then the sum of the other two roots is ______.

Options

• 4

• –3

• 2

• 5

Answer 1

If x = –4 is a root of `|(x, 2, 3),(1, x, 1),(3, 2, x)| = 0`, then the sum of the other two roots is 4.

Explanation:

Given, `|(x, 2, 3),(1, x, 1),(3, 2, x)| = 0`

`\implies` x(x² – 2) – 2(x – 3) + 3(2 – 3x) = 0

`\implies` x³ – 13x + 12 = 0

Since (x + 4) is one root of above cubic equation.

Sum roots = 0

∴ Sum of two roots + (– 4) = 0

Sum of two roots = 4