How do you begin to solve x^3-3x^2 > x-3?
1 answer:
For any polynomial, first check to see if it factors. Then you can set each factor equal to zero.
The three zeros are -1,1,3
Next plug in values in each interval between zeros to test whether its greater than 0.
Try x values: -2,0,2,4
x = -2 yields a negative result, the interval x< -1 is Not a solution.
x = 0 yields a positive result, the interval -1
x = 2 yields a negative result, the interval 1
x = 4 yields a positive result, the interval x>3 IS a solution
The three zeros are -1,1,3
Next plug in values in each interval between zeros to test whether its greater than 0.
Try x values: -2,0,2,4
x = -2 yields a negative result, the interval x< -1 is Not a solution.
x = 0 yields a positive result, the interval -1
x = 2 yields a negative result, the interval 1
x = 4 yields a positive result, the interval x>3 IS a solution
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Answer: The required length of the segment AA' is 11 units.
Step-by-step explanation: Given that the point A(5, 11) is reflected across the X-axis.
We are to find the length of the segment AA'.
We know that
if a point (x, y) is reflected across X-axis, then its co-ordinates becomes (x, -y).
So, after reflection, the co-ordinates of the point A(5, 11) becomes A'(5, -11).
Now, we have the following distance formula :
The DISTANCE between two points P(a, b) and Q(c, d) gives the length of the segment PQ as follows :
Therefore, the length of the segment AA' is given by
Thus, the required length of the segment AA' is 11 units.