Advertisements
Advertisements
प्रश्न
What number should be added to polynomial f(x)= 12x3 + 16x2 - 5x - 8 so that the resulting polynomial is exactly divisible by (2x - 1) ?
Advertisements
उत्तर
(2x - 1) ⇒ x = `1/2`
When we substirute this value in the polynomial, whatever we get as a remainder (say a) should be added so that polynomial is exactly subtracted by the factor.
`"f"(1/2) = 12 xx (1/2) xx (1/2) xx (1/2) + 16 xx (1/2) xx (1/2) - 5 xx (1/2) - 8 + "a" = 0`
`=> 3/2 + 4 - 5/2 - 8 + "a" = 0`
⇒ a = 5
+ 4 - - 8 + a = Hence answer = 5
APPEARS IN
संबंधित प्रश्न
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 1
If x3 + ax2 + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
A polynomial f(x) when divided by (x - 1) leaves a remainder 3 and when divided by (x - 2) leaves a remainder of 1. Show that when its divided by (x - i)(x - 2), the remainder is (-2x + 5).
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
