Podcast
Questions and Answers
Solve the inequality $x^2 + 6x + 8 < 0$
Solve the inequality $x^2 + 6x + 8 < 0$
$-4 < x < -2$
Solve the inequality $x^2 - 9x + 14 \le 0$
Solve the inequality $x^2 - 9x + 14 \le 0$
$2 \le x \le 7$
Solve the inequality $x^2 > 4(8 - x)$
Solve the inequality $x^2 > 4(8 - x)$
$x < -8$ or $x > 4$
Solve the inequality $3x^2 - 5x - 1 < 4x^2 + 7x + 19$
Solve the inequality $3x^2 - 5x - 1 < 4x^2 + 7x + 19$
Find the set of values of x for which $x^2 - 2x - 24 < 0$ and $12 - 5x \ge x + 9$
Find the set of values of x for which $x^2 - 2x - 24 < 0$ and $12 - 5x \ge x + 9$
Find the set of values of x for which $x^2 - 100 > 0$ and $x^2 + 8x - 105 > 0$
Find the set of values of x for which $x^2 - 100 > 0$ and $x^2 + 8x - 105 > 0$
Flashcards
Quadratic Inequality
Quadratic Inequality
A quadratic inequality involves comparing a quadratic expression to a value using inequality symbols.
Solving Quadratic Inequalities
Solving Quadratic Inequalities
To solve a quadratic inequality, rearrange it to have zero on one side, factorize, find critical values, and test intervals.
Critical Values
Critical Values
The values of x where the quadratic expression equals zero.
Testing Intervals
Testing Intervals
After finding critical values, test values from each interval in the original inequality to determine which intervals satisfy the inequality.
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Expressing the Solution Set
Expressing the Solution Set
Express the solution set using inequality notation or interval notation, indicating which intervals satisfy the original inequality.
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- The resource focuses on solving quadratic inequalities.
- Revision for this topic can be found at www.corbettmaths.com/contents, Video 378.
Solving Quadratic Inequalities
- To solve x² + 6x + 8 < 0:
- Factorize to get (x+2)(x+4) = 0.
- Solutions are x = -2 and x = -4.
- The solution to the inequality is -4 < x < -2.
- To solve x² + 2x – 35 > 0:
- Factorize to get (x+7)(x-5) = 0.
- Solutions are x = -7 and x = 5.
- The solution to the inequality is x < -7 or x > 5.
- To solve x² – 9x + 14 ≤ 0:
- Factorize to get (x-7)(x-2) = 0.
- Solutions are x = 7 and x = 2.
- The solution to the inequality is 2 ≤ x ≤ 7.
- To solve x² – x – 30 ≥ 0:
- Factorize to get (x-6)(x+5) = 0.
- Solutions are x = 6 and x = -5.
- The solution to the inequality is x ≤ -5 or x ≥ 6.
- To solve x² > 4(8 – x):
- Rearrange and factorize to get (x+8)(x-4) = 0.
- Solutions are x = -8 and x = 4.
- The solution to the inequality is x < -8 or x > 4.
- To solve 3x² – 5x – 1 < 4x² + 7x + 19:
- Simplify and factorize to get (x+2)(x+10) = 0.
- Solutions are x = -2 and x = -10.
- The solution to the inequality is x < -10 or x > -2.
- To solve 2x² + 9x + 10 > 0:
- Factorize to get (2x + 5)(x + 2) = 0.
- Solutions are x = -5/2 and x = -2.
- The solution to the inequality is x < -5/2 or x > -2.
- To solve 7x² - 22x + 16 ≤ 0:
- Factorize to get (7x-8)(x-2) = 0.
- Solutions are x = 8/7 and x = 2.
- The solution to the inequality is 8/7 ≤ x ≤ 2.
Finding the set of values of x
- To find the set of values of x for which x² - 2x – 24 < 0 and 12 – 5x ≥ x + 9:
- First inequality: Factorize to get (x-6)(x+4) = 0, solutions x = 6 and x = -4, so -4 < x < 6.
- Second inequality: Solve 12 – 5x ≥ x + 9 to get x ≤ 1/2.
- Combine: -4 ≤ x ≤ 1/2.
- To find the set of values of x for which x² - 100 > 0 and x² + 8x – 105 > 0:
- First inequality: Factorize to get (x-10)(x+10) = 0, solutions x = 10 and x = -10, so x < -10 or x > 10.
- Second inequality: Factorize to get (x-7)(x+15) = 0, solutions x = 7 and x = -15, so x < -15 or x > 7.
- Combine: x < -15 or x > 10.
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