Quadratic Equations

What is quadratic equation?

A polynomial equation of the second degree in one variable is called the quadratic equation. The general form of the quadratic equation is ax² + bx + c = 0. Here, a and b are the coefficients of x² and x terms respectively, and c is the constant term.

What is standard form of quadratic equation?

Standard Form of Quadratic Equation is ax² + bx + c = 0

Give some examples of quadratic equations.

Some examples of quadratic equations are :

• 2x² -x + 2
• 4x² – 13x + 33= 0
• 8x² = 0
• 13x² -17 = 0

What is quadratic formula?

General formula to solve a quadratic equation of the form ax² + bx + c = 0 is 

x = [-b ± √(b² – 4ac)]/2a

What is discriminant of quadratic equation?

For any quadratic equation of the form ax² + bx + c = 0, we calculate the value b² – 4ac this is called the discriminant of the quadratic equation. It is denoted by D. It is used to tell the nature of the roots of the quadratic equation.

What are the roots of quadratic equation?

The roots of a quadratic equation are the values of x that satisfy the equation ax² + bx + c = 0 where, a, b, and c are Real Numbers and Constants and a ≠ 0.

How to factor a quadratic equation?

To factor a quadratic equation of the form, ax² + bx +c =0:

1. Find two numbers that multiply to ac (the product of the coefficient of x² and the constant term) and add to b (the coefficient of x).
2. Rewrite the middle term (bx) as the sum of two terms using the numbers found in step 1.
3. Factor by grouping.

How is quadratic equation different from linear equation?

Quadratic Equation differs from Linear Equation in the manner that Quadratic Equation has degree two and can have maximum of two solutions while Linear Equation has degree one and can have only one solution at maximum.

How to solve quadratic equations graphically?

While solving Quadratic Equation ax² + bx + c = 0 graphically we need to find where the curve of the quadratic equation cuts the x-axis. The coordinates at which the curve of the quadratic equation cuts the x-axis are the roots of the quadratic equations.

How to solve quadratic equations?

Quadratic equations can be solved using various methods, including factoring, completing the square, using the quadratic formula, or by graphing.

How to solve quadratic equations by factoring?

To solve quadratic equations by factoring, first set the equation to ax²+bx+c=0. Then, factor the quadratic expression into two binomial factors. Finally, solve for the variable x by setting each factor equal to zero and solving for x.

A Quadratic equation is a second-degree equation that can be represented as ax² + bx + c = 0. In this equation, x is an unknown variable, a, b, and c are constants, and a is not equal to 0. To solve it, you can use methods such as factoring, completing the square, or the quadratic formula. Each method helps find the values of x that satisfy the equation.

Let’s learn how to solve Quadratic Equations using different methods in detail.