Advertisements
Advertisements
प्रश्न
f(x) = x3 − 6x2 + 2x − 4, g(x) = 1 − 2x
उत्तर
Let us denote the given polynomials as
`f(x) = x^3 - 6x^2 + 2x - 4`
`g(x) = 1-2x`
`⇒ g(x) = -2 (x - 1/2)`
We have to find the remainder when f(x)is divided by g(x).
By the remainder theorem, when f(x) is divided by g(x)the remainder is
`f(1/2) = (1/2)^3 -6 (1/2)^2 + 2(1/2) - 4`
` = 1/8 - 6 xx 1/4 + 2 xx 1/2 - 4`
` = 1/8 - 3/2 + 1 - 4`
` = 1/8 - 3/2 - 3`
`= - 35/8`
Now we will calculate remainder by actual division
So the remainder is `(-35)/8`.
APPEARS IN
संबंधित प्रश्न
Write the degrees of each of the following polynomials
`7x3 + 4x2 – 3x + 12`
Find the remainder when x3 + 3x2 + 3x + 1 is divided by \[x + \pi\] .
The polynomials ax3 + 3x2 − 3 and 2x3 − 5x + a when divided by (x − 4) leave the remainders R1 and R2 respectively. Find the value of the following case, if R1 = R2.
Find the values of a and b so that (x + 1) and (x − 1) are factors of x4 + ax3 − 3x2 + 2x + b.
If both x + 1 and x − 1 are factors of ax3 + x2 − 2x + b, find the values of a and b.
x4 − 7x3 + 9x2 + 7x − 10
Define zero or root of a polynomial.
Find the remainder when x3 + 4x2 + 4x − 3 is divided by x.
Mark the correct alternative in each of the following:
If x − 2 is a factor of x2 + 3ax − 2a, then a =
If x51 + 51 is divided by x + 1, the remainder is
