Quadratic Inequalities

What do we call these symbols < , > , ≥ , ≤ ?

• Equality Symbols

• Inequality Symbols

• Unequality Symbols

• Signs

Answer explanation

The symbols <, >, ≥, and ≤ are used to compare values, indicating relationships of less than, greater than, and their inclusive forms. Therefore, they are correctly referred to as Inequality Symbols.

• Quadratic Equation

• Quadratic Inequality

• Linear Inequality

• Linear Equation

Answer explanation

The given forms represent inequalities involving a quadratic expression, which is defined as a quadratic inequality. This distinguishes it from linear equations or inequalities, making 'Quadratic Inequality' the correct choice.

Which of the following mathematical statements is a quadratic inequality?

Answer explanation

A quadratic inequality is an inequality involving a quadratic expression. The correct choice, 3t^2+7t+2≥0, is a quadratic inequality, while the others are either equations or linear inequalities.

• QUADRATIC INEQUALITY

• NOT QUADRATIC INEQUALITY

Answer explanation

The expression \( (2x-3)(x+2) > 0 \) is a product of two linear factors, which defines a quadratic inequality. Therefore, the correct choice is QUADRATIC INEQUALITY.

• QUADRATIC INEQUALITY

• NOT QUADRATIC INEQUALITY

Answer explanation

The expression 12x + 18 < 0 is a linear inequality, not a quadratic one. Quadratic inequalities involve terms with x squared (e.g., ax^2 + bx + c < 0). Therefore, the correct choice is NOT QUADRATIC INEQUALITY.

• I only

• II only

• I and II only

• I and III only

Answer explanation

I. is a quadratic inequality (\(x^2 + 8x + 12 \ge 0\)). II. is an equation, not an inequality. III. is also a quadratic inequality (\(x^2 - 1 < 0\)). Thus, the correct answer is I and III only.

• QUADRATIC INEQUALITY

• NOT QUADRATIC INEQUALITY

Answer explanation

The inequality can be simplified to 0 < 2x - 4, which is linear, not quadratic. A quadratic inequality involves a squared term, but here, the squared terms cancel out, confirming it is NOT a quadratic inequality.

• QUADRATIC INEQUALITY

• NOT QUADRATIC INEQUALITY

Answer explanation

The expression simplifies to a quadratic form, as it includes a term with $x^2$. Therefore, it represents a quadratic inequality, confirming the correct choice is 'QUADRATIC INEQUALITY'.

Which of the following inequalities is the same as 2x² + 4x - 6 < 0 ?

• 2(x - 1)(x + 3) < 0

• (2x - 3)(x + 2) < 0

• (2x + 2)(x - 3) < 0

• 2(x + 6)(x - 1) < 0

Answer explanation

To solve 2x² + 4x - 6 < 0, we factor it as 2(x - 1)(x + 3) < 0. This shows the correct choice is 2(x - 1)(x + 3) < 0, as it matches the original inequality.

What are the values of the variable that make quadratic inequalities true called?

• Solutions or Roots

• Extraneous Roots

• Quadratic Solutions

• Rational Solutions

Answer explanation

The values that satisfy quadratic inequalities are called "Solutions or Roots". These terms refer to the points where the quadratic expression equals zero or meets the inequality condition.