The roots of f(x) are {0, 3, -4}. You've got them as {-3, 4}, which is not correct.
Draw another set of coordinate axes and place dark dots at (0,0), (3,0) and (-4,0). These dots represent the roots (solutions) of the given polynomial.
Note that we have a repeated (double) root at x=3, which is given away by the exponent 2 of (x-3).
A basic way of sketching this graph is described as follows:
Evaluate the function (find y) for several x-values other than (0, 3 and -4):
Choose (for example) {-5, -2, -1, 1, 2, 4}
If you'll find the y-value for each of these x-values and plot the resulting points, you should see the shape of the graph. Draw a rough graph thru these points. If any doubt remains about what the graph looks like at particular x-values, calculate and plot more points, e. g., at {-2.5, -1.5, ...}.
If you're taking calculus, consider applying the First- and Second-Derivative tests to determine concavity, maximum, minimum, etc.
Answer:
-3/4 is plotted 3 little tabs left of 0
5/4 is plotted 1 little tab right of 1
Answer:
-3x is the answer I'm pretty sure I think
<h3>
Answer: 226 degrees</h3>
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Explanation:
Notice the tickmarks on the segments in the diagram. This tells us that chords DC and CB are the same distance from the center. It furthermore means that DC and CB are the same length, and arcs DC and CB are the same measure
arc DC = arc CB
12x+7 = 18x-23
12x-18x = -23-7
-6x = -30
x = -30/(-6)
x = 5
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Use this x value to find the measure of arcs DC and CB
- arc DC = 12x+7 = 12*5+7 = 67
- arc CB = 18x-23 = 18*5-23 = 67
We get the same measure for each, which helps confirm we have the correct x value.
The two arcs in question add to 67+67 = 134 degrees. This is the measure of arc DCB. Subtract this from 360 to get the answer
arc DAB = 360-(arc DCB) = 360-134 = 226 degrees
I'm using the idea that (arc DCB) + (arc DAB) = 360 since the two arcs form a full circle.
"The discriminant is prime?" I haven't heard that one before.
Here are the general rules:
1. a positive discriminant results in two real, unequal roots.
2. a zero discr. results in two real, equal roots.
3. a negative discr. results in two complex roots, which sometimes means two imaginary roots.
