### Theory:

In earlier classes, you have learned a variety of polynomials. For example, the quadratic polynomial of the form $$ax^2 + bx + c$$, $$a \ne 0$$ was one kind. We get a quadratic equation when we equate this polynomial to zero.

Let's see a conversation between two friends to understand the concept of the quadratic equation.

Aathira: Hi! Bhuvana.

Bhuvana: Hi! Aathira, you look so great!! What's special today?

Aathira: It's my birthday.

Bhuvana: I wish you a happy birthday, Aathira!

Aathira: Thank you, Bhuvana!

Bhuvana: How old are you?

Aathira: I'll give you a hint about my age. Try to find it.

Bhuvana: Ohh! I like solving puzzles. Tell me quickly.

Aathira: I'm two years younger than my brother, and the product of my age and my brother's age is $$80$$. Could you find out how old I am?

Bhuvana: Let me take your brother age is $$x$$ years. So, your's $$x - 2$$ years.

Product of your ages $$=$$ $$80$$

$$x (x -2) = 80$$

$$x^2 - 2x = 80$$

$$x^2 - 2x - 80 = 0$$

$$x = -8$$ and $$x = 10$$

Bhuvana: Age cannot be a negative number. So, your brother was $$10$$ years old, and you are $$10 - 2 = 8$$ years old.

Aathira: Aww!!!! That's right!!! How do you find it?