**Table of Contents**

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**Introduction**

The word "**Quadratic**" is derived from the word "**Quad**" which means square.

In other words, a quadratic equation is an “**equation of degree 2**.”

There are many scenarios where quadratic equations are used.

Did you know that when a rocket is launched, its path is described by a quadratic equation?

**Definitions and Examples**

**An equation of the form \(ax^2+bx+c=0\), where \(a \neq 0\) is called a quadratic equation.**

Here are some examples of equations:

Equations | Values of \(a\), \(b\) and \(c\) | |
---|---|---|

1. | \(8x^2+7x-1=0\) | \[\begin{align}a&=8 \\b&=7 \\c&=-1 \end{align}\] |

2. | \(4x^2-9=0\) | \[\begin{align}a&=4 \\b&=0 \\c&=-9 \end{align}\] |

3. | \(x^2+x=0\) | \[\begin{align}a&=1 \\b&=1 \\c&=0 \end{align}\] |

4. | \(6x-8=0\) | \[\begin{align}a&=0 \\b&=6 \\c&=-8 \end{align}\] |

Look at Example 4.

Here, \(a = 0\). Therefore, it is not a quadratic equation.

The remaining equations are quadratic equation examples.

### Practice Problems on Quadratic Equations

1. The sum and product of zeros of a quadratic polynomial f(x) are S = -8/3 and P = 4/3 respectively. Write the correct expression for f(x) if its constant term is 4.

- 3x
^{2}+ 8x + 4 - 3x
^{2}+ 8x - 4 - 3x
^{2}-8x + 4 - 8x
^{2}+ 3x + 4

**Check Answer:-**

**Answer: 1**

2. If (x + 4) is the factor of the equation px^{2} + 6x + 8q = 0, then which of the following relations is correct?

- p - q = 3
- 2p - q = 4
- 2p + q = 3
- p + 2q = 6

**Check Answer:-**

**Answer: 3**

3. The sum of the squares of the zeros of x^{2} - 8x + p = 0 is 40. What is the value of p?

- 12
- 8
- 120
- 3

**Check Answer:-**

**Answer: 1**

4. Choose the correct option for the quadratic equation x^{2} + 3x - 4 = 0

- The value of the discriminant is 25
- The quadratic expression has non-real and distinct zeroes
- The quadratic expression has real and equal zeroes
- The value of the discriminant is -25

**Check Answer:-**

**Answer: 1**

5. For what values of k, does the quadratic equation x^{2} + (2K - 1)x + K^{2} = 0 have real and equal roots?

- K < -1/4
- K = 4
- K = 1/4
- K < -4

**Check Answer:-**

**Answer: 3**