Advertisements
Advertisements
प्रश्न
If (x + 2) and (x + 3) are factors of x3 + ax + b, find the values of ‘a’ and ‘b’.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
Find the value of a, if x – 2 is a factor of 2x5 – 6x4 – 2ax3 + 6ax2 + 4ax + 8.
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
(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.
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Prove by factor theorem that
(2x - 1) is a factor of 6x3 - x2 - 5x +2
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
Use factor theorem to factorise the following polynominals completely.
x3 + 2x2 – 5x – 6
If (3x – 2) is a factor of 3x3 – kx2 + 21x – 10, find the value of k.
