select the values of ^xthat are the solutions to inequality 0>x^2+5x-2
x^2 + 5x - 2 < 0
Solve and graph: x^2 + 5x - 2 = 0
Use Quadratic Formula an get:
X = -5.37, and 0.372
Solution to inequality:-5.37 < X < 0.372
To find the values of x that are the solutions to the inequality 0 > x^2 + 5x - 2, we can follow these steps:
Step 1: Start by setting the quadratic equation equal to zero: x^2 + 5x - 2 = 0.
Step 2: Solve the quadratic equation for its roots. You can do this by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula in this case.
The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
For our equation x^2 + 5x - 2 = 0, the quadratic formula becomes:
x = (-5 ± √(5^2 - 4(1)(-2))) / (2(1))
= (-5 ± √(25 + 8)) / 2
= (-5 ± √33) / 2
Step 3: Now, we have two possible values for x: (-5 + √33) / 2 and (-5 - √33) / 2.
Step 4: Analyze the sign of the inequality 0 > x^2 + 5x - 2 for different intervals.
To do this, we can create a number line and mark the critical points (-5 + √33) / 2 and (-5 - √33) / 2 on it.
Number line:
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(-5 - √33) / 2 (-5 + √33) / 2
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Step 5: Choose a test value for each interval and substitute it into the quadratic inequality to see if it satisfies the condition.
For example, let's choose x = 0, which falls between (-5 - √33) / 2 and (-5 + √33) / 2.
Substituting x = 0 into the inequality 0 > x^2 + 5x - 2:
0 > (0)^2 + 5(0) - 2
0 > 0 - 2
0 > -2
Since 0 is greater than -2, the inequality is satisfied.
Step 6: Based on the results of the test values, we can conclude that the values of x that satisfy the inequality 0 > x^2 + 5x - 2 are all real numbers that fall within the intervals (-5 - √33) / 2 < x < (-5 + √33) / 2.