Advertisements
Advertisements
प्रश्न
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3) x – 6 leave the same remainder. Find the value of ‘p’.
उत्तर
If (x – 3) divides f(x) = x3 – px2 + x + 6, then,
Remainder = f(3) = 33 – p(3)2 + 3 + 6 = 36 – 9p
If (x – 3) divides g(x) = 2x3 – x2 – (p + 3) x – 6, then
Remainder = g(3) = 2(3)3 – (3)2 – (p + 3) (3) – 6 = 30 – 3p
Now, f(3) = g(3)
⇒ 36 – 9p = 30 – 3p
⇒ -6p = -6
⇒ p = 1
APPEARS IN
संबंधित प्रश्न
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 − 19x + 6
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
When x3 + 3x2 – mx + 4 is divided by x – 2, the remainder is m + 3. Find the value of m.
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).
use the rernainder theorem to find the factors of ( a-b )3 + (b-c )3 + ( c-a)3
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).
Find the value of p if the division of px3 + 9x2 + 4x - 10 by (x + 3) leaves the remainder 5.
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 4x2 + 5x + 3
