Advertisements
Advertisements
प्रश्न
If the polynomial y3 − 5y2 + 7y + m is divided by y + 2 and the remainder is 50 then find the value of m.
Advertisements
उत्तर
Let p(y) = y3 − 5y2 + 7y + m
When the polynomial is divided by (y + 2), the remainder is 50. This means that the value of the polynomial when y = −2 is 50.
By remainder theorem,
Remainder = p(−2) = 50
∴ (−2)3 − 5 × (−2)2 + 7 (−2) + m = 50
⇒ − 8 − 5 × 4 -14 + m = 50
⇒ − 8 − 20 − 14 + m = 50
⇒ − 42 + m = 50
⇒ m = 50 + 42 = 92
Thus, the value of m is 92.
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by 5 + 2x.
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
Using the remainder theorem, find the remainders obtained when x3 + (kx + 8 )x + k is divided by x + 1 and x − 2.
Hence, find k if the sum of the two remainders is 1.
Find without division, the remainder in the following:
5x3 - 7x2 +3 is divided by (x-1)
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).
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.
What number should be added to 2x3 - 3x2 + 7x -8 so that the resulting polynomial is exactly divisible by (x-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).
Find the remainder (without division) on dividing f(x) by (2x + 1) where f(x) = 3x3 – 7x2 + 4x + 11
Find the remainder (without division) when 2x3 – 3x2 + 7x – 8 is divided by x – 1 (2000)
When a polynomial f(x) is divided by (x – 1), the remainder is 5 and when it is,, divided by (x – 2), the remainder is 7. Find – the remainder when it is divided by (x – 1) (x – 2).
What is the remainder when x2018 + 2018 is divided by x – 1
The polynomial p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7 when divided by x + 1 leaves the remainder 19. Find the values of a. Also find the remainder when p(x) is divided by x + 2.
