Advertisements
Advertisements
Question
Find ‘a‘ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leave the same remainder when divided by x + 3.
Solution
`x+3=0` ⇒ `x=-3`
Since, the given polynomials leave the same remainder when dividend by (x-3),
value of polynomial `ax^3+3x^2-9` at x=-3 is sae as value of polynomial `2x^3+4x+a at x=-3`
⇒ `a(-3)^3+3(-3)^2-9=2(-3)^3+4(-3)++a`
⇒`-27a+27-9=-54-12+a`
⇒`-27a+18=-66+a`
⇒`28a=84`
⇒`a=84/28`
⇒a=3
APPEARS IN
RELATED QUESTIONS
Using remainder theorem, find the value of k if on dividing 2x3 + 3x2 – kx + 5 by x – 2, leaves a remainder 7.
Find 'a' if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
Use the Remainder Theorem to find which of the following is a factor of 2x3 + 3x2 – 5x – 6.
x + 2
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 23x – 30
Using the Remainder Theorem, factorise the expression 3x3 + 10x2 + x – 6. Hence, solve the equation 3x3 + 10x2 + x – 6 = 0
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).
Using remainder theorem, find the remainder on dividing f(x) by (x + 3) where f(x) = 3x3 + 7x2 – 5x + 1
Find ‘a’ if the two polynomials ax3 + 3x2 – 9 and 2x3 + 4x + a, leaves the same remainder when divided by x + 3.
