A is a quadratic coefficient, b is a linear coefficient and c is a constant.

The unary quadratic AX 2+BX+C = 0 can be solved by formula x=, which is a formula that directly represents the root with the coefficient of the equation. This formula was given by Al Khorezmo of Central Asia as early as the 9th century.

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Although Arabs mastered the solution of quadratic equation in the ninth century.

But the most important theory of univariate quadratic equation was established by the French mathematician Veda, who discussed the relationship between the roots and coefficients of the equation in On the Identification and Correction of Equations, and this important result was also named Vieta Theorem.

The formula for finding the root of a quadratic equation with one variable

To discuss the properties of arbitrary equations, we need a solution that can be used for all equations.

For a quadratic equation with one variable, we only need to first convert the general formula of the corresponding quadratic function into a vertex type, and then solve it by square root:

Among them? δ determines whether the equation can successfully complete the operation of square root, which is called the discriminant of root.

What if? δ& gt； 0? Then we can square smoothly and calculate two solutions of x, which can also be called two roots.

What if? δ& lt； 0? Negative numbers cannot be squared, and the equation has no solution in the range of real numbers.

Especially? Δ=0? We say that the two solutions of the equation are the same size, which is called multiple roots.

The Inverse Theorem of Vieta Theorem

If we have a quadratic equation, we can find the sum and product of two roots by Vieta theorem.

On the other hand, if we know the sum and product of two roots, we can construct the corresponding quadratic equation of one variable and solve it.

People want to know whether there is any connection between higher order polynomials and quadratic polynomials.

For a rational polynomial of degree n with n roots, it must be decomposed into a series of products of linear or quadratic rational polynomials, that is, one rational root corresponds to a linear polynomial and a pair of irrational roots corresponds to a quadratic polynomial.

Further using complex numbers to solve the problem of no real roots can prove that polynomial of degree n can be decomposed into the product of a series of linear or quadratic polynomials, that is, a real root corresponds to a linear polynomial and a pair of complex roots corresponds to a quadratic polynomial.