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
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x+1.
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Using the Remainder and Factor Theorem, factorise the following polynomial:
`x^3 + 10x^2 - 37x + 26`
Use the Remainder Theorem to factorise the following expression:]
`2x^3 + x^2 - 13x + 6`
Find the remainder when x4 – 3x2 + 2x + 1 is divided by x – 1.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
2x – 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:
3x3 + 2x2 – 23x – 30
For what value of m is x3 – 2mx2 + 16 divisible by x + 2?
