Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, p(x) = x4 – 2x3 + 3x2 – ax + 3a – 7
When we divide p(x) by x + 1, then we get the remainder p(–1).
Now, p(–1) = (–1)4 – 2(–1)3 + 3(–1)2 – a(–1) + 3a – 7
= 1 + 2 + 3 + a + 3a – 7
= 4a – 1
p(–1) = 19
⇒ 4a – 1 = 19
⇒ 4a = 20
∴ a = 5
∴ Required polynomial = x4 – 2x3 + 3x2 – 5x + 3(5) – 7 ...[Put a = 5 on p(x)]
= x4 – 2x3 + 3x2 – 5x + 15 – 7
= x4 – 2x3 + 3x2 – 5x + 8
When we divide p(x) by x + 2, then we get the remainder p(–2)
Now, p(–2) = (–2)4 – 2(–2)3 + 3(–2)2 – 5(–2) + 8
= 16 + 16 + 12 + 10 + 8
= 62
Hence, the value of a is 5 and remainder is 62.
APPEARS IN
संबंधित प्रश्न
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Using the Remainder Theorem, factorise the following completely:
4x3 + 7x2 – 36x – 63
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 subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x - 4
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + 2
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
What is the remainder when x2018 + 2018 is divided by x – 1
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
