Advertisements
Advertisements
प्रश्न
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).
उत्तर
(2x +3) ⇒ x = `-3/2` .....(i)
(x + 2) ⇒ x = - 2 ...(ii)
putting (i) in polynomial , we get
`"f"(-3/2) = "a" xx (-3/2) xx (-3/2) xx (-3/2) + 3 xx (-3/2) xx (-3/2) + "b" xx (-3/2) - 3 = 0`
- 27 a + 54 - 12 b - 24 = 0
⇒ 27 a = -12 b + 30 ....(iii)
Putting (ii) in polynomial, and remainder is -3 we get
f(-2) = a × (-2) × (-2) × (-2) + 3 × (-2) × (-2) + b× (-2) - 3 = -3
b = 6 - 4a ..... (iv)
Combining (iii) and (iv), we get,
27a = -12 ×(6 - 4a) + 30
⇒ 27a= -72 + 48a + 30,
⇒ a=2, b= 6-4x2 = -2
a= 2, b= -2
APPEARS IN
संबंधित 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.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
If p(x) = 4x3 - 3x2 + 2x - 4 find the remainderwhen p(x) is divided by:
x + `(1)/(2)`.
When divided by x – 3 the polynomials x3 – px2 + x + 6 and 2x3 – x2 – (p + 3)x – 6 leave the same remainder. Find the value of ‘p’.
Find the remainder when 2x3 – 3x2 + 4x + 7 is divided by x + 3
If x51 + 51 is divided by x + 1, the remainder is ______.
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
If x25 + x24 is divided by (x + 1), the result is ______.
