Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
It is given that when the polynomial x3 + 2x2 – 5ax – 7 is divided by (x – 1), the remainder is A.
∴ (1)3 + 2(1)2 – 5a(1) – 7 = A
1 + 2 – 5a – 7 = A
–5a – 4 = A ...(i)
It is also given that when the polynomial x3 + ax2 – 12x + 16 is divided by (x + 2), the remainder is B.
∴ x3 + ax2 – 12x + 16 = B
(–2)3 + a(–2)2 – 12(–2) + 16 = B
–8 + 4a + 24 + 16 = B
4a + 32 = B ...(ii)
It is also given that 2A + B = 0
Using (i) and (ii), we get,
2(–5a – 4) + 4a + 32 = 0
–10a – 8 + 4a + 32 = 0
–6a + 24 = 0
6a = 24
a = 4
APPEARS IN
संबंधित प्रश्न
Use Remainder theorem to factorize the following polynomial:
`2x^3 + 3x^2 - 9x - 10`
Find the remainder when x4 + 1 is divided by x + 1.
When x3 + 2x2 – kx + 4 is divided by x – 2, the remainder is k. Find the value of constant k.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
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).
Find the values of a and b when the polynomial f(x)= ax3 + 3x2 +bx -3 is exactly divisible by (2x+3) and leaves a remainder -3 when divided by (x+2).
What number must be subtracted from 2x2 – 5x so that the resulting polynomial leaves the remainder 2, when divided by 2x + 1 ?
Using the Remainder Theorem, factorise completely the following polynomial:
3x2 + 2x2 – 19x + 6
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x – 2
What must be subtracted from the polynomial x3 + x2 – 2x + 1, so that the result is exactly divisible by (x – 3)?
