Quadratic equations — lesson. Mathematics CBSE, Class 10.

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A quadratic equation in the variable

$x$ is an equation of the form

$ax^2 + bx + c = 0$ , where

$a$ ,

$b$ ,

$c$ are real numbers,

$a ≠ 0$ . The degree of the quadratic equation is

$2$ .

Important!

The equation

$ax^2 + bx + c = 0$ is called the standard form of a quadratic equation.

Example:

1. Check whether the equation

$(x - 3)^2 + 2 = 3x - 4$ is a quadratic or not.

Solution:

$(x - 3)^2 + 2 = 3x - 4$

$\Rightarrow x^2 - 6x + 9 + 2 = 3x - 4$

$\Rightarrow x^2 - 6x + 11 - 3x + 4 = 0$

$\Rightarrow x^2 - 9x + 15 = 0$

It is of the form

$ax^2 + bx + c = 0$ .

Therefore, the given equation is a quadratic equation.

2. Check whether the equation

$x(x + 2) + 6 = x^2 - 3x + 4$ is a quadratic or not.

Solution:

$x(x + 2) + 6 = x^2 - 3x + 4$

$\Rightarrow x^2 + 2x + 6 = x^2 - 3x + 4$

$\Rightarrow x^2 + 2x + 6 - x^2 + 3x - 4 = 0$

$\Rightarrow 5x + 2 = 0$

Here, the degree of the equation is

$1$ .

Therefore, the given equation is not a quadratic equation.

Did you find an error?

2. Quadratic equations