The sum-of-two formula is X1+X2=-(b/a) and the product-of-two formula is X1*X2=c/a. The sum-of-two and product-of-two formulas are found in quadratic equations. An integer equation that contains two unknowns and the number of terms containing the unknowns is 1 is called a quadratic equation.

: The value of each pair of unknowns that fits into a quadratic equation is called a solution of that quadratic equation. Each quadratic equation has an infinite number of pairs of solutions, and it is the system of quadratic equations composed of quadratic equations that may have a unique solution. A system of quadratic equations is often converted to a quadratic equation for solution by addition, subtraction and elimination or substitution and elimination.

The sum of the two roots = -b/a; the product of the two roots = c/a. An equation containing two unknowns, and the number of terms containing the unknowns is 1, is called a quadratic equation. All quadratic equations can be reduced to the general form of ax+by+c=0 (a, b≠0) and the standard form of ax+by=c (a, b≠0), otherwise they are not quadratic equations.

The derivation goes like this: the quadratic equation ax?+bx + c = 0 if it has two roots x1 and x2, then it can be written as a(x-x1)(x-x2) = 0. Simplifying it, we get: ax?-a(x1 + x2) + ax1x2 = 0. So -a(x1 + x2) = b, and ax1x2 = c. Solving: x1+x2 = -b/a and x1x2 = c/a.

Knowing the sum of the two roots of a quadratic equation and the product of the two roots,how to find the expression of the equation:Vedic Theorem: 1. Assume that the quadratic equation ax2+bx+C = 0 (a is not equal to 0) 2. The two roots of the equation x1, x2 and the coefficients of the equation, a, b, and c, then satisfy: 3, x1+x2=-b/a, x1x2=c/a. According to x1+x2=-b/a, x1x2=c/a. you can find x1 and x2, and then finally the expression of the equation according to the two roots of the equation: a(x-x1)(x-x2)=0.

Solution of quadratic equations: I. Direct open square method Shape of (x + a)^2 = b, when b is greater than or equal to 0, x + a = positive or negative root sign b, x = -a plus or minus root sign b; when b is less than 0. The equation has no real roots. II.MATCHING METHODS 1. quadratic coefficients to 1 2. shift terms, quadratic and primary on the left, constant on the right. 3. formulate the equation by adding the square of half of the coefficient of the primary term on both sides to the form (x=a)^2=b. 4. use the direct squaring method to solve the equation. Third, the formula method The equation is now organized into the general form: ax^2 + bx + c = 0. Then substitute abc into the formula x=(-b±√(b^2-4ac))/2a, (b^2-4ac is greater than or equal to 0). Fourth, the factorization method If the quadratic equation ax^2 + bx + c = 0, such as the number of the left side of the algebraic formula is easy to decompose, then give priority to the factorization method.

Personal advice: in the sum of the two roots and the product of the two roots, be sure to pay attention to the symbols, to avoid the wrong result because of carelessness.