This is a free lesson from our course in Algebra II
In this section, you'll learn how to find the quadratic equation if roots are given. Consider the quadratic equation ax^{2} + bx + c. Suppose that its roots are denoted by and . Then
• the sum of the roots is +
• the product of the roots is
The quadratic equation can be formed by using the formula: x^{2}  (sum of roots)x + (product of roots).
(More text below video...)
(Continued from above)
When the quadratic equation with rational coefficients has radical roots, the roots are conjugate of one another.For example, 2 +
3
is a root of the equation; other root is the conjugate of 2 +
3,
i.e. 2 
3.
To find the equation in this example, find the sum of roots i.e.
2 +
3
+ 2 
3
= 4,
and product of roots i.e.
(2 +
3)
(2 
3)
= (2)2  (3)2
= 1,
which gives the quadratic equation as x^{2}  4x + 1
= 0.
The same is true if the roots are complex, e.g. for the roots 5 + 3i and 5  3i,
the quadratic equation is x^{2}  10x + 34 = 0.
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