Advertisements
Advertisements
Question
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).
Solution
(2x + 1) ⇒ x = `-1/2`
Solving equation (i), we get
`"f"(-1/2) = 2 xx (-1/2) xx (-1/2) - 5 xx (-1/2) + "a" = 0`
`=> 1/2 + 5/2 + "a" = 0`
⇒ a = -3
`"g" (-1/2) = 2 xx (-1/2) xx (-1/2) + 5 xx (-1/2) + "b" = 0`
`=> 1/2 - 5/2 + "b" = 0`
⇒ b = 2
⇒ a = -3 , b = 2
APPEARS IN
RELATED QUESTIONS
What must be subtracted from 16x3 – 8x2 + 4x + 7 so that the resulting expression has 2x + 1 as a factor?
What number should be added to 3x3 – 5x2 + 6x so that when resulting polynomial is divided by x – 3, the remainder is 8?
What number should be subtracted from x3 + 3x2 – 8x + 14 so that on dividing it by x – 2, the remainder is 10?
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
Using the Remainder Theorem, factorise the following completely:
x3 + x2 – 4x – 4
Find without division, the remainder in the following:
5x2 - 9x + 4 is divided by (x - 2)
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).
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
When 2x3 – 9x2 + 10x – p is divided by (x + 1), the remainder is – 24.Find the value of p.
