Polynomial Question (1 Viewer)

[tekster]

The following question was in my 3u half yearly today.

Find all possible values of a and b for the polynomial, (x - a) + b if:
- the polynomial is equal to zero for x = 1
- when divided by x, the remainder is -7

 

[~To...=~]

well...

(x - a)^3 + b... mmm

since x = 1 is a zero,

(1 - a)^3 + b = 0

1 - 3a + 3a^2 - a^3 + b = 0 ... Q


now, when divided by x, the remainder is -7

by division of polynomials,

[ (x - a)^3 + b ] / x = S(x) - a^3 + b, where S(x) is another is the quotient.

clearly, the remainder is R(x) = - a^3 + b = -7 ... W

now, Q - W :

1 - 3a + 3a^2 = 7

3a^2 -3a - 6 = 0

a^2 - a - 2 = 0

( a + 1 ) ( a - 2) = 0

therefore,

a = -1, b = -8

or

a = 2, b = 1

mmm...i think dats right...well, dats wat i got so i hope dats rite...keke

does this help joe...hehe