Polynomial: 2x2 + 3x – 5 < 0 in this interval: -5/2 < x < 1,
POLYNOMIAL INEQUALITIES
> means left side is greater than right side
< means left side is less than right side
Example1:
Solve: 2x2 + 3x – 5 < 0
y = 2x2 + 3x – 5 = (2x + 5)(x - 1) = 0
Roots of the equation: x1 = - 5/2 and x2 = 1
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|
x < - 5/2 |
x = -5/2 |
-5/2 < x < 1 |
x = 1 |
1 < x |
|
Sign of (2x + 5) |
- |
0 |
+ |
+ |
+ |
|
Sign of (x - 1) |
- |
- |
- |
0 |
+ |
|
Sign of (2x + 5)(x - 1) |
+ |
0 |
- |
0 |
+ |
|
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Polynomial: 2x2 + 3x – 5 < 0 in this interval: -5/2 < x < 1,
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Example 2:
2x4 – x3 – 47 x2 + x + 45 > 0
Factor: y = (2x + 9)(x - 5)(x - 1)(x + 1) = 0
Roots: x1 = - 4.5, x2 = 5, x3 = 1, x4 = -1
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From the graph, Polynomial:
2x4 – x3 – 47 x2 + x + 45 > 0
in these intervals: x < -4.5, -1 < x < 1, 5 < x
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