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