How to find the sum of the roots of the equation

Determining the amount of roots of the equation - one of the necessary steps in solving quadratic equations (equations of the form ax2 + bx + c = 0, where the coefficients a, b, and c are arbitrary numbers, with a ≠ 0) using the theorem of vieta.

Instruction

1. Write the quadratic equation in the form ax2 + bx + c = 0
   
   Example:
   Original equation: 12 + x2= 8x
   Correct the equation: x2 - 8x + 12 = 0
2. Apply the vieta theorem, according to which the sum of the roots of the equation will be equal to the number "b", taken with the opposite sign, and their work - a "c".
   
   Example:
   In this equation b=-8, c=12, respectively:
   x1+x2=8
   x1∗x2=12
3. Learn positive and negative numbers are roots of equations. If the product and the sum of the roots is positive number, each of the roots is positive. If the product of the roots is positive and the sum of the roots is negative, then both root – negative. If the product of the roots is negative, the roots one root is the " + " sign and another sign "-" In this case, you must use an additional rule: "If the sum of the roots is a positive number greater than the module root is also positive and if the sum of the roots is negative - the larger the module root is negative."
   
   Example:
   In this equation the sum and product of positive numbers: 8 and 12, then both the root - the positive number.
4. Solve this system of equations by choosing from the roots. Will be convenient to begin with the selection of the multipliers, and then, to check, substitute each pair of multipliers into the second equation and test whether the sum of these roots solution.
   
   Example:
   x1∗x2=12
   Suitable pairs of roots are respectively: 12 and 1, 6 and 2, 4 and 3
   
   Check out the pair using equation x1+x2=8. Pair
   12 + 1 ≠ 8
   6 + 2 = 8
   4 + 3 ≠ 8
   
   Accordingly, the roots of an equation are numbers 6 and 8.