# What is a quadratic inequality in algebra?

## What is a quadratic inequality in algebra?

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign. Examples of quadratic inequalities are: x2 – 6x – 16 ≤ 0, 2×2 – 11x + 12 > 0, x2 + 4 > 0, x2 – 3x + 2 ≤ 0 etc. Solving a quadratic inequality in Algebra is similar to solving a quadratic equation.

### What is the formula of quadratic inequality?

A quadratic inequality is an inequality that contains a quadratic expression. The graph of a quadratic function f(x)=ax2+bx+c=0 is a parabola. When we ask when is ax2+bx+c<0, we are asking when is f(x)<0. We want to know when the parabola is below the x-axis.

Which of the mathematical statements is a quadratic inequality?

A quadratic inequality is a mathematical statement that relates a quadratic expression as either less than or greater than another. A solution to a quadratic inequality is a real number that will produce a true statement when substituted for the variable.

What are the 5 ways to solve a quadratic equation?

There are several methods you can use to solve a quadratic equation: Factoring Completing the Square Quadratic Formula Graphing

• Factoring.
• Completing the Square.
• Graphing.

## What is a basic algebra equation?

Basic Of Algebra. Basics of Algebra cover the simple operation of mathematics like addition, subtraction, multiplication, and division involving both constant as well as variables. For example, x+10 = 0. This introduces an important algebraic concept known as equations.

### How many solutions does a quadratic inequality have?

Quadratic inequalities can have infinitely many solutions, one solution or no solution. We can solve quadratic inequalities graphically by first rewriting the inequality in standard form, with zero on one side. Graph the quadratic function and determine where it is above or below the x-axis.

How to Solve a Quadratic Inequality in Factored Form. Step 1: Set the first factor equal to zero, and solve for the variable. Step 2: Set the second factor equal to zero, and solve for the

What are the rules of solving inequalities?

Add the same number on both sides.

• From both sides,subtract the same number.
• By the same positive number,multiply both sides.
• By the same positive number,divide both sides.
• Multiply the same negative number on both sides and reverse the sign.
• ## What is the formula for solving quadratic equations?

– Quadratic formula If your equation is ax^2 + bx + c use: x = (-b +- sqrt (b^2 – 4ac)) / 2a – Factoring If your equation is eg x^2 + 13x – 30 = 0 Factor the constant term→ -30 = +15*-2 and 13 = +15-2 (x+15) (x-2) Needs a bit of – Completing the square If your equation is eg x^2 + 2x – 11 = 0 Re-write it as x^2 + 2x = 11 x^2 + 2x + 1 = 11

### How to solve quadratic equations quickly?

– Method 1: factorizing by trial and error. Let us think about the example above, of the equation . – Method 2: some kinds of quadratic equations are easy to solve. A quadratic equation doesn’t have to be in the form . – Method 3: completing the square. – Method 4: the quadratic formula. – Method 5: Turn the equation into a different problem and then solve it.

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