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
Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.
If x – 2 is a factor of x2 + ax + b and a + b = 1, find the values of a and b.
Using the factor Theorem, show that:
2x + 7 is a factor 2x3 + 5x2 − 11x – 14. Hence, factorise the given expression completely.
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 x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Check if (x + 2) and (x – 4) are the sides of a rectangle whose area is x2 – 2x – 8 by using factor theorem
If x – 3 is a factor of p(x), then the remainder is
Find the value of 'a' if x – a is a factor of the polynomial 3x3 + x2 – ax – 81.
