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
3a = 6
a = 2
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
so the third root is x=3/2
= (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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