18 - Writing Quadratic Equations when Given its Roots - Part 1

In this lesson, we will write quadratic equations when given the roots of the function. We will discuss that any pair of roots actually yields an infinite family of quadratic functions that pass through those roots.

We discuss what this actually means, how to find the family of functions, and how to find a specific quadratic that passes through those roots. We will also graph these quadratic functions.

[amberbazanx]

I adopted you as my dad, you are encouraging and smart. You have helped me tremendously and I appreciate you!! Thank you Jason aka Math Daddy!!!

[MintyRBXWasTaken]

thank you!! i was so so so confused because my math teacher couldnt explain it but you explained it so well!!

[motherofpearls]

Good stuff Jason!! I wish I had of found this type of help earlier during my son’s school year. #enlightenment 😃 💡

[rahmatabadi]

There are infinitely many quadratic equations with roots (or zeros) of 1 and 5.
They are k(x^2-6x+5)=0 for any non zero k.

In order to make the solution unique, so you need to say "Find a quadratic equation whose coefficient of x^2 is 1 and roots are 1 and 5", for example.

[davidben]

Thank you Sir have a wonderful Christmas and a healthy and a happy new year to and your family.
From the UK.

[alphasaffi]

Thank you sir we need more examples on this topics.

[hemarajue]

Do mean by the theorem, if the given roots are rational we need to multiply the factors with their LCDs to get into a standard form of quadratic equation ?

[daliamarshall]

How can u because a member on your wed site

[farhadkhalasi]

This theorem is easy to understand but there is one more thing that when we multiply by a, this generates a family of quadratics with the same roots r1and r2 in general.

[shanettateague]

I'm still not understanding these