Posted by **JASLEEN** on Wednesday, June 6, 2012 at 3:23am.

two zeros of cubic polynomial ax^3+3x^2-bx-6 are -1 and -2. find the third zero and values of a and b

- MATHS -
**Reiny**, Wednesday, June 6, 2012 at 8:59am
if x=-1, then -a + 3 + b - 6 = 0

a - b = -3

if x=-2, then -8a + 12 + 2b - 6 = 0

8a - 2b = 6

4a - b = 3

subtract them:

3a = 6

a = 2

in a-b=-3

2-b = -3

b = 5

so expression is

2x^3 + 3x^2 - 5x - 6

which is (x+1)(x+2)( ?x + ?)

by common sense, the last bracket must be

(2x -3)

so the third root is x=3/2

check:

(x+1)(x+2)(2x-3)

= (x^2 + 3x + 2)(2x-3)

= 2x^3 - 3x^2 + 6x^2 - 9x + 4x - 6

= 2x^3 + 3x^2 - 5x - 6 , all is good

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