Algebra II: Finding a Quadratic Equation given the roots
 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 ax2 + 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: x2 - (sum of roots)x + (product of roots). (More text below video...)
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(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 x2 - 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 x2 - 10x + 34 = 0.
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