Question

If x = −2 is one root of x³ − x² − 17x = 22, then find the other roots of equation

Answer 1

Let f(x) = x³ – x² – 17x – 22 = 0   .....(1)

Given that x = – 2 is a root of f(x).

∴ x + 2 is a factor of f (x)

Using synthetic division

Comparing equation (1) with the equation ax² + bx + c = 0

We have a = 1, b = – 3, c = – 11

x = `(-"b" +-  sqrt("b"^2 - 4"ac"))/(2"a")`

∴ x = `(-(- 3) +-  sqrt((- 3)^2 - 4(1)(- 11)))/(2 xx 1)`

x = `(3 +-  sqrt(9 + 44))/2`

= `(3 +-  sqrt(53))/2`

Hence the other roots are `(3 + sqrt(53))/2, (3 - sqrt(53))/2`