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# How to form Quadratic Equation from given Roots?

TopA Quadratic Equation is the algebraic equation, which is expressed in the form of ax2 + bx + c = 0, such that a, b, c are the integers and a <> 0. In case we talk about the roots of the equation, it means the values which are the solution to the given equation. Any quadratic equation can have at the most two roots. Let us now learn how to form quadratic equation from given roots. If we are not given the equations and only the roots are given as α and β. The values of α and β can be real and equal or sometimes real and unequal. Further we need to find the equation for the given roots, then in such a situation, we will first add the roots of the given equation as α + β and the product of the roots as α * β. So once the sum of roots and the product of the roots is calculated, we can form the quadratic equation as:
X2 - sum of roots. x + product of roots = 0
Now let us consider the example, where the two roots of the quadratic equations are 2 and -3 i.e. values of α and β are given.
Now we will first find the sum of roots as α + β = 2 + ( -3 ) = -1 and the product of the roots is given as α * β = 2 * ( -3 ) = -6
Thus we say that the quadratic equation so formed will be:
X2 – ( -1 ) x + ( -6) = 0
X2 + x – 6 = 0
Thus we say that the above equation is the quadratic equation, which is formed when the sum of the roots and the product of the roots are known. These roots were real and unequal