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: - 8x2 + 5x + 9 = 0 is an example of a quadratic equation 

Standard form of quadratic equation

The standard form of the quadratic equation is  ax2 + bx + c = 0, a ≠ 0.
Example: -
The quadratic equation 13x2 - 9x + 6 = 0 is in the standard form.
Lets consider a few  examples
Example 1: -
Write the quadratic equation in standard form.
9x2 = 7x + 5
Solution: -
We know that the standard form of the quadratic equation is given by ax2 + bx + c = 0, a ≠ 0.
Given equation is 9x2 = 7x + 5
To convert this to standard form, we take all terms to left.
Subtracting 7x and 5 on both sides, we get
9x2 - 7x - 5 = 0, which is the required standard form

Example 2: -
Write the quadratic equation in standard form.
12x = 3x2 - 8
Solution: -
We know that the standard form of the quadratic equation is given by ax2 + bx + c = 0, a ≠ 0.
Given equation is 12x = 3x2 - 8
To convert this to standard form, we take all terms to the right.
Subtracting 12 from both sides, we get
3x2 - 12x - 8 = 0, which is the required standard form

Example 3: -

Write the quadratic equation in standard form.
12x2 - x = 5
Solution: -
We know that the standard form of the quadratic equation is given by ax2 + bx + c = 0, a ≠ 0.
Given equation is 12x2 - x = 5
To convert this to standard form, we take all terms to left.
Subtracting  5 from both sides, we get
12x2 - 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 ax2 + 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. 4x2 = 2x + 1
b. 4x = 3x2 - 10
c. 11x2 - 9x = 8
d.  3x - 7x = 15
Answers: -
a. 4x2 - 2x - 1 = 0
b. 3x2 - 4x - 10 = 0
c. 11x2 - 9x - 8 = 0
d. Not a quadratic equation