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) ?
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 x3 + 3x2 + 3x + 1 is divided by x+1.
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
Find the value of ‘m’, if mx3 + 2x2 – 3 and x2 – mx + 4 leave the same remainder when each is divided by x – 2.
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Find the values of a and b when the factors of the polynomial f(x)= ax3 + bx2 + x a are (x+3) and (2x-1). Factorize the polynomial completely.
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).
When x3 + 3x2 – kx + 4 is divided by (x – 2), the remainder is k. Find the value of k.
Find the remainder when the polynomial f(x) = 2x4 - 6x3 + 2x2 - x + 2 is divided by x + 2.
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’.
