Question

If (x + 2) and (x + 3) are factors of x³ + ax + b, find the values of ‘a’ and ‘b’.

Answer 1

Given (x + 2) is a factor of `x^3 + ax + b`

`=> (-2)^3 + a(-a) + b = 0`       ...(x + 2 = 0 ⇒ x = -2)

`=> -8-2a + b = 0`

`=> -2a + b = 8`        ...(1)

Also, given that (x+ 3) is a factor of x³ + ax + b

`=> (-3)^3 + a(-3) + b = 0`

`=> -27 - 3a + b = 0`

`=> -3a + b = 27`      ...(2)

Subtracting (1) from (2) we have

`-a = 19 => a = -19`

Substituting a = -19 in (1), we have

`-2 xx (-19) + b = 8`

`=> 38 + b = 8`

`=> b = -30``

Hence, a = -19 and b = -30