Finding a quadratic equation when sum and product of its roots are given

This post is very much reverse engineering of quadratic equations. We are given with sum of roots and product of the roots. We have to find the quadratic equation then its roots.

Let me explain it by taking an example;

Find a quadratic equation having sum and product of its roots -3 and -4 respectively. Then find the roots of the equation.

Solution: Consider “p” and “q” be the two roots of the given equation.

Now we know that sum of roots = -3

Which means                       p + q = -3

Also product of roots = -4

Which means         pq = -4

When “p” and “q” are the roots of the quadratic equation we can write the following;

(x – p) (x – q) = 0

x² - xq – px +pq = 0  

x² - (p + q)x + pq = 0

But we know that “p+q = -3” and “pq = -4”

x² - (-3)x + (-4) = 0

x² + 3x – 4 = 0

Above is the required quadratic equations

Now we can solve this equation to find its roots.  I will use the factor method to solve it;

(x – 1) (x + 4) = 0

Either   x – 1 = 0      OR    x + 4 = 0

x = 1, - 4 are the roots of the given equation.      

Below are the links to my previous posts on quadratic equations;

https://steemit.com/steemiteducation/@mathworksheets/finding-a-quadratic-equation-whose-roots-are-given

 https://steemit.com/steemiteducation/@mathworksheets/sum-and-product-of-roots-of-a-quadratic-equation  

https://steemit.com/steemiteducation/@mathworksheets/solving-quadratic-equations-using-the-formula  

https://steemit.com/steemiteducation/@mathworksheets/discriminant-and-nature-of-roots-of-a-quadratic-equation

https://steemit.com/steemiteducation/@mathworksheets/the-quadratic-formula-let-s-drive-it  

https://steemit.com/steemiteducation/@mathworksheets/quadratic-equations-solve-by-completing-the-square-method

https://steemit.com/steemiteducation/@mathworksheets/completing-the-square-of-a-quadratic-equation-3  

https://steemit.com/steemiteducation/@mathworksheets/solving-quadratic-equations-by-completing-the-square-2

https://steemit.com/steemiteducation/@mathworksheets/solving-quadratic-equations-by-completing-the-square-1

https://steemit.com/steemiteducation/@mathworksheets/completing-the-square-of-a-quadratic-equation-algebrically

https://steemit.com/steemiteducation/@mathworksheets/completing-the-square-of-a-quadratic-function-geometrically

https://steemit.com/steemiteducation/@mathworksheets/how-to-solve-quadratic-equations-using-the-factoring-method

https://steemit.com/steemiteducation/@mathworksheets/graphing-the-simplest-quadratic-function  

https://steemit.com/steemiteducation/@mathworksheets/quadratic-functions-an-introduction