Question
One zero of f(x)=2x3−x2−2x+1
is -1. What are the other zeros of the function?
(1 point)
Responses
1 and 2
1 and 2
2 and 12
2 and 1 half
1 and 12
1 and 1 half
1 and 3
To find the other zeros of the function, we can use polynomial long division or synthetic division to divide the polynomial by the linear factor (x + 1).
Using synthetic division, we have:
-1 | 2 -1 -2 1
-2 3 -1
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2 -3 1 0
The resulting quotient is 2x^2 - 3x + 1. To find the zeros of this quadratic polynomial, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the quadratic polynomial 2x^2 - 3x + 1, a = 2, b = -3, and c = 1.
Plugging these values into the quadratic formula, we have:
x = (3 ± √((-3)^2 - 4(2)(1))) / (2(2))
= (3 ± √(9 - 8)) / 4
= (3 ± √1) / 4
= (3 ± 1) / 4
So the other zeros of the function are:
x = (3 + 1) / 4 = 4 / 4 = 1
x = (3 - 1) / 4 = 2 / 4 = 1/2
Therefore, the other zeros of the function are 1 and 1/2.
The correct answer is: 1 and 1/2.