Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero.
1) f(x)= 3(x^2 +1)^2
2) f(x)= -4(x+2)(x-5)^3
Two math questions
2008-04-09 9:51 pm
回答 (1)
2008-04-09 11:23 pm
✔ 最佳答案
1) f(x) = 3(x^2+1)^2 It is always greater than 3. There is no zeros.
It will not cross the x-axis.
2) f(x) = -4(x+2)(x-5)^3
Its zeros occur when x = -2 with multiplicity 1 and 5 with multiplicity 3
When x is slightly less than -2, f(x) <0
When x is slightly larger than -2, f(x) >0.
f(x) crosses the x-axis at x = -2
When x is slightly less than 5, f(x) >0
When x is slightly larger than 5, f(x) <0
f(x) crosses the x-axis at x = 5
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