Advertisements
Advertisements
प्रश्न
What number should be subtracted from the polynomial f(x)= 2x3 - 5x2 +8x -17 so that the resulting polynomial is exactly divisible by (2x - 5)?
Advertisements
उत्तर
(2x - 5) = 0 ⇒ x = `5/2`
When we substitute this value in the polynomial, whatever we get as a remainder (say a) should be subtracted so that polynomial is exactly subtracted by the factor.
`"f" (5/2) = 2 xx (5/2) xx (5/2) xx (5/2) - 5 xx (5/2) xx (5/2) + 8 xx (5/2) - 17 - "a" = 0`
`=> 125 /4 - 125/4 + 20 - 17 - "a" = 0`
⇒ a = 3
Hence answer = 3
APPEARS IN
संबंधित प्रश्न
Check whether 7 + 3x is a factor of 3x3 + 7x.
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
When the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A and when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B. Find the value of ‘a’ if 2A + B = 0.
Find the values of p and q in the polynomial f(x)= x3 - px2 + 14x -q, if it is exactly divisible by (x-1) and (x-2).
Using remainder theorem, find the value of a if the division of x3 + 5x2 – ax + 6 by (x – 1) leaves the remainder 2a.
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
When 2x3 – x2 – 3x + 5 is divided by 2x + 1, then the remainder is
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 3x2 + 4x + 50; g(x) = x – 3
