#Class10Mathematics #Chapter2 #Exercise2b #Qno7 #Qno8 #qno9 #qno10

What is a quadratic equation? A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b and c being constants, or numerical coefficients, and x being an unknown variable. Keep reading for examples of quadratic equations in standard and non-standard forms, as well as a list of quadratic equation terms.

Standard Form Equation Examples
The easiest way to learn quadratic equations is to start in standard form. While not every quadratic equation you see will be in this form, it's still helpful to see examples. Keep in mind that the first constant a cannot be a zero.

Examples of the standard form of a quadratic equation (ax² + bx + c = 0) include:

6x² + 11x - 35 = 0
2x² - 4x - 2 = 0
-4x² - 7x +12 = 0
20x² -15x - 10 = 0
x² -x - 3 = 0
5x² - 2x - 9 = 0
3x² + 4x + 2 = 0
-x² +6x + 18 = 0
Incomplete Quadratic Equation Examples
As you develop your algebra skills, you'll find that not every quadratic equation is in the standard form. Check out examples of several different instances of non-standard quadratic equations.

Missing the Linear Coefficient
Sometimes a quadratic equation doesn't have the linear coefficient or the bx part of the equation. Examples include:

2x² - 64 = 0
x² - 16 = 0
9x² + 49 = 0
-2x² - 4 = 0
4x² + 81 = 0
-x² - 9 = 0
3x² - 36 = 0
6x² + 144 = 0
Missing the Constant Term
Quadratic equations can also lack the constant term, or c. For example:

x² - 7x = 0
2x² + 8x = 0
-x² - 9x = 0
x² + 2x = 0
-6x² - 3x = 0
-5x² + x = 0
-12x² + 13x = 0
11x² - 27x = 0
Quadratic Equation Examples in Factored Form
Factoring is one way to solve a quadratic equation. Here are examples of quadratic equations in factored form:

(x + 2)(x - 3) = 0 [standard form: x² - 1x - 6 = 0]
(x + 1)(x + 6) = 0 [standard form: x² + 7x + 6 = 0]
(x - 6)(x + 1) = 0 [standard form: x² - 5x - 6 = 0]
-3(x - 4)(2x + 3) = 0 [standard form: -6x² + 15x + 36 = 0]
(x − 5)(x + 3) = 0 [standard form: x² − 2x − 15 = 0]
(x - 5)(x + 2) = 0 [standard form: x² - 3x - 10 = 0]
(x - 4)(x + 2) = 0 [standard form: x² - 2x - 8 = 0]
(2x+3)(3x - 2) = 0 [standard form: 6x² + 5x - 6]
Examples of Quadratic Equations in Other Forms
Examples of quadratic equations in other forms include:

x(x - 2) = 4 [upon multiplying and moving the 4, becomes x² - 2x - 4 = 0]
x(2x + 3) = 12 [upon multiplying and moving the 12, becomes 2x² - 3x - 12 = 0]
3x(x + 8) = -2 [upon multiplying and moving the -2, becomes 3x² + 24x + 2 = 0]
5x² = 9 - x [moving the 9 and -x to the other side, becomes 5x² + x - 9]
-6x² = -2 + x [moving the -2 and x to the other side, becomes -6x² - x + 2]
x² = 27x -14 [moving the -14 and 27x to the other side, becomes x² - 27x + 14]
x² + 2x = 1 [moving "1" to the other side, becomes x² + 2x - 1 = 0]
4x² - 7x = 15 [moving 15 to the other side, becomes 4x² + 7x - 15 = 0]
-8x² + 3x = -100 [moving -100 to the other side, becomes -8x² + 3x + 100 = 0]
25x + 6 = 99 x² [moving 99 x2 to the other side, becomes -99 x² + 25x + 6 = 0]