Advertisements
Advertisements
प्रश्न
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
उत्तर
Let f(x) = ax3 + 3x2 – 3
When f(x) is divided by (x – 4), remainder = f(4)
f(4) = a(4)3 + 3(4)2 – 3 = 64a + 45
Let g(x) = 2x3 – 5x + a
When g(x) is divided by (x – 4), remainder = g(4)
g(4) = 2(4)3 – 5(4) + a = a + 108
It is given that f(4) = g(4)
64a + 45 = a + 108
63a = 63
a = 1
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by `x - 1/2`
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
If x3 + ax2 + bx + 6 has x – 2 as a factor and leaves a remainder 3 when divided by x – 3, find the values of a and b.
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
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.
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 remainder when 2x3 – 3x2 + 4x + 7 is divided by 2x + 1
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
Without actual division, prove that 2x4 – 5x3 + 2x2 – x + 2 is divisible by x2 – 3x + 2. [Hint: Factorise x2 – 3x + 2]
