Advertisements
Advertisements
प्रश्न
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Advertisements
उत्तर
Let f(x) = ax3 + 9x2 + 4x – 10
x + 3 = 0
`\implies` x = –3
On dividing f(x) by x + 3, it leaves a remainder 5.
∴ f(–3) = 5
a(–3)3 + 9(–3)2 + 4(–3) – 10 = 5
–27a + 81 – 12 – 10 = 5
-27a + 81 - 22 = 5
-27a + 59 = 5
-27a = 5 - 59
-27a = -54
a = `(-54)/-27`
a = 2
संबंधित प्रश्न
Find the remainder when x3 + 3x2 – 12x + 4 is divided by x – 2.
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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Use remainder theorem and find the remainder when the polynomial g(x) = x3 + x2 – 2x + 1 is divided by x – 3.
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
If on dividing 4x2 – 3kx + 5 by x + 2, the remainder is – 3 then the value of k is
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x + 3
Check whether p(x) is a multiple of g(x) or not:
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
Check whether p(x) is a multiple of g(x) or not:
p(x) = 2x3 – 11x2 – 4x + 5, g(x) = 2x + 1
