Advertisements
Advertisements
Question
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Advertisements
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
APPEARS IN
RELATED QUESTIONS
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
What should be subtracted from 3x3 – 8x2 + 4x – 3, so that the resulting expression has x + 2 as a factor?
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Prove by factor theorem that
(3x-2) is a factor of 18x3 - 3x2 + 6x -12
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
Use factor theorem to factorise the following polynominals completely. x3 – 13x – 12.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
