## Quadratic equation

A polynomial of second degree is called a quadratic polynomial. Any equation f(x) = 0 where f is a quadratic polynomial is called a quadratic equation.

Example: - 8x^{2 }+ 5x + 9 = 0 is an example of a quadratic equation

## Standard form of quadratic equation

^{2}+ bx + c = 0, a ≠ 0.

Example: -

The quadratic equation 13x

^{2}- 9x + 6 = 0 is in the standard form.

Lets consider a few examples

**Example 1: -**

Write the quadratic equation in standard form.

9x

^{2}= 7x + 5

**Solution: -**

We know that the standard form of the quadratic equation is given by ax

^{2}+ bx + c = 0, a ≠ 0.

Given equation is 9x

^{2}= 7x + 5

To convert this to standard form, we take all terms to left.

Subtracting 7x and 5 on both sides, we get

**9x**

^{2}- 7x - 5 = 0, which is the required standard form**Example 2: -**

Write the quadratic equation in standard form.

^{}12x = 3x

^{2}- 8

**Solution: -**

We know that the standard form of the quadratic equation is given by ax

^{2}+ bx + c = 0, a ≠ 0.

Given equation is 12x = 3x

^{2}- 8

To convert this to standard form, we take all terms to the right.

Subtracting 12 from both sides, we get

**3x**

^{2}- 12x - 8 = 0, which is the required standard form

Example 3: -

Example 3: -

Write the quadratic equation in standard form.

12x

^{2}- x = 5

**Solution: -**

We know that the standard form of the quadratic equation is given by ax

^{2}+ bx + c = 0, a ≠ 0.

Given equation is 12x

^{2}- x = 5

To convert this to standard form, we take all terms to left.

Subtracting 5 from both sides, we get

**12x**

^{2}- x - 5 = 0, which is the required standard form**Example 4: -**

Write the equation in standard form.

9x

^{}= 7x + 5

**Solution: -**

We know that the standard form of the quadratic equation is given by ax

^{2}+ bx + c = 0, a ≠ 0.

Given equation is 9x = 7x + 5

Note that there is no second degree term. So we cannot write this in standard form.

Try Yourself: -

Write the following equations in standard form: -

a. 4x

^{2}= 2x + 1

b. 4x = 3x

^{2}- 10

c. 11x

^{2}- 9x = 8

d. 3x - 7x = 15

Answers: -

a. 4x

^{2}- 2x - 1 = 0

b. 3x

^{2}- 4x - 10 = 0

c. 11x

^{2}- 9x - 8 = 0

d. Not a quadratic equation