Math Problem Statement
Solution
The problem in the image asks:
Which of the following value of do not satisfy the inequality at all?
The options are:
a)
b)
c)
d)
Solution:
We start by solving the quadratic inequality .
Step 1: Solve
Factoring the quadratic equation:
So, the roots of the equation are and .
Step 2: Analyze the sign of
Now, we need to determine where the quadratic expression is positive. We will check the intervals defined by the roots:
-
For , pick :
So, the inequality is satisfied for . -
For , pick :
So, the inequality is not satisfied for . -
For , pick :
So, the inequality is satisfied for .
Step 3: Combine results
The inequality is satisfied for:
The inequality is not satisfied for .
Conclusion:
The correct answer is a) , as this interval does not satisfy the inequality at all.
Would you like a more detailed explanation or have any questions?
Here are 5 related questions for further practice:
- Solve .
- Solve the inequality .
- Find the values of that satisfy .
- For what values of is ?
- Solve the quadratic inequality .
Tip: When solving quadratic inequalities, it helps to plot the parabola or analyze sign changes at the roots.
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Math Problem Analysis
Mathematical Concepts
Quadratic Inequality
Algebra
Factoring
Formulas
Quadratic equation formula: ax^2 + bx + c = 0
Theorems
Factorization of quadratic equations
Suitable Grade Level
Grades 8-10