Understanding Quadratic Inequalities

The video tutorial explains how to solve the inequality x^2 + 3x > 10. It begins by transforming the inequality into a more familiar quadratic form by subtracting 10 from both sides. The quadratic expression is then factored, and reasoning is applied to determine the solution set. The tutorial discusses the conditions under which the product of two expressions is greater than zero, leading to the solution x > 2 or x < -5. Finally, the solution set is represented on a number line.

What is the first step suggested to solve the inequality x^2 + 3x > 10?

• Multiply both sides by 2

• Divide both sides by x

• Subtract 10 from both sides

• Add 10 to both sides

When factoring the expression x^2 + 3x - 10, which pair of numbers is used?

• 1 and 10

• 2 and 5

• 5 and -2

• 3 and -3

What must be true about two numbers if their product is greater than zero?

• They must have opposite signs

• They must both be zero

• One must be zero

• They must have the same sign

If x + 5 > 0 and x - 2 > 0, what can be concluded about x?

• x > 5

• x > 2

• x < -5

• x < 2

What is the simplified condition for x if x + 5 < 0 and x - 2 < 0?

• x < -5

• x < 2

• x > -5

• x > 2

What is the solution set for the inequality x^2 + 3x > 10?

• x > 5 or x < -2

• x < 5 or x > -2

• x > 2 or x < -5

• x < 2 or x > -5

How is the solution set represented on a number line?

• Open circle at 2, closed at -5

• Closed circles at 2 and -5

• Open circles at 2 and -5

• Closed circle at 2, open at -5

Which of the following values satisfies the inequality x^2 + 3x > 10?

• x = 1

• x = -6

• x = -4

• x = 0

What is the result of substituting x = 3 into the inequality x^2 + 3x > 10?

• 21

• 18

• 12

• 9

Which of the following is NOT a part of the solution set for x^2 + 3x > 10?

• x = 4

• x = 0

• x = -6

• x = 3