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).
Advertisements
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
Find the remainder when x3 – ax2 + 6x – a is divided by x – a.
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
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.
Using the Remainder Theorem, factorise the following completely:
2x3 + x2 – 13x + 6
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.
(x2 − 7x + 9) ; (x + 1)
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(2x3 − 2x2 + ax − a) ; (x − a)
Find the values of m and n when the polynomial f(x)= x3 - 2x2 + m x +n has a factor (x+2) and leaves a remainder 9 when divided by (x+1).
What number should be subtracted from x2 + x + 1 so that the resulting polynomial is exactly divisible by (x-2) ?
What number must be added to 2x3 – 7x2 + 2x so that the resulting polynomial leaves the remainder – 2 when divided by 2x – 3?
