Advertisements
Advertisements
Question
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of 'a' and `b'.
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
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
If 2x + 1 is a factor of 2x2 + ax – 3, find the value of a.
Prove by factor theorem that
(x - 3) is a factor of 5x2 - 21 x +18
Find the value of m ·when x3 + 3x2 -m x +4 is exactly divisible by (x-2)
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
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
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
For what value of k is the polynomial p(x) = 2x3 – kx2 + 3x + 10 exactly divisible by (x – 2)
Factors of 3x3 – 2x2 – 8x are ______.
If mx2 – nx + 8 has x – 2 as a factor, then ______.
