What is the universal formula of a binary quadratic equation, and what is the universal formula meth

The universal formula for the unary quadratic equation ax 2+bx+c=0 x=(-b (b 2-4ac)) 2a.

Solution: For the unary quadratic equation ax 2+bx+c=0(a≠0), it can be simplified to obtain x 2+b a*x+c a=0

x^2+2*b/2a*x+(b/a)^2-(b/2a)^2+c/a=0

x+b/2a)^2=(b/2a)^2-c/a

i.e. (x+b 2a) 2=(b 2-4ac) a 2

Then we can get x+b 2a= (b 2-4ac)) 2a, or x+b 2a=- (b 2-4ac)) 2a.

Then x=(-b+ (b 2-4ac)) 2a, or x=(-b- (b 2-4ac)) 2a.

So the universal solution formula for a quadratic equation is x=(-b (b 2-4ac)) 2a.

For one-dimensional quadratic equations.

ax^2+bx+c=0.(a is not 0).

When b -4ac <0, the equation has no solution:

When b -4ac 0, x = [-b (b -4ac)] 2a

A quadratic equation won't solve? Just remember this root-finding formula, and you'll be able to do it!

Binary Linear EquationsMagna formula：b^2-4ac>=0。

An integer equation that contains two unknowns, and the term containing the unknowns is 1 in degree, is called a binary linear equation. The value of an unknown that equalizes the left and right sides of the equation is called the solution of the equation.

Equations have real roots.

Otherwise it's an imaginary number.

Root. The real solution is: [-b+sqrt(b 2-4ac)] 2a, [-b-sqrt(b 2-4ac)] 2a.

The meaning of binary linear equations.

An integer equation code book that contains two unknowns, and the order of the term that contains the unknown's delay macro is 1, is called a binary equation. All binary linear equations can be reduced to the general expression of ax+by+c=0(a, b≠0) and the standard expression of ax+by=c(a, b≠0), otherwise they are not binary linear equations.

The value that fits each pair of unknowns of a binary equation is called a solution of the binary equation. Each binary linear equation has an infinite number of solutions to the equation, consisting of a system of binary linear equations.

Only a system of binary equations may have a unique solution, and a system of binary equations is often converted into a unitary equation by addition and subtraction or substitution of the elimination method.

to solve.

Binary one-time square dispersion frontUniversal formula: b 2-4ac>=0, the equation has a real root, otherwise it isImaginary numbersRoot.

The solution to the real number is: -b+sqrt(b 2-4ac)] 2a.

b-sqrt(b^2-4ac)]/2a。

Solve the equation:The value that fits each pair of unknowns of a binary equation is called a solution of the binary equation. For any binary cubic square perturbation, if one of the unknowns takes any value, the value of the other unknown corresponding to it can be found.

Suspicious. Therefore, any binary linear equation has an infinite number of solutions, and the set of these solutions is called the solution set of this binary linear equation.

Universal formula: unary quadratic equation formula: x=(-b (b 2-4ac)) 2a. That is, an integral equation that contains only one unknown number (unary number) and the maximum number of oak heights of the unknown terms is 2 (quadratic) is called a quadratic equation.

where ax is called the quadratic term, and a is the quadratic coefficient; bx is called the primary term, and b is the coefficient of the primary term; c is called a constant term.

An equation is an equation that contains unknowns. It is an equation that expresses the equality relationship between two mathematical formulas (such as two numbers, functions, quantities, operations), and the value of the unknown number that makes the equation true is called the "solution" or "root". The process of finding the solution of the equation is called "solving the square and setting the equation".

The universal formula for the unary quadratic equation ax 2+bx+c=0 x=(-b (b 2-4ac)) 2a.

Solution: For the unary quadratic equation ax 2+bx+c=0(a≠0), it can be simplified to obtain x 2+b a*x+c a=0

x^2+2*b/2a*x+(b/a)^2-(b/2a)^2+c/a=0

x+b/2a)^2=(b/2a)^2-c/a

i.e. (x+b 2a) 2=(b 2-4ac) a 2

Then we can get x+b 2a= (b 2-4ac)) 2a, or x+b 2a=- (b 2-4ac)) 2a.

Then x=(-b+ (b 2-4ac)) 2a, or x=(-b- (b 2-4ac)) 2a.

So the universal solution formula for a quadratic equation is x=(-b (b 2-4ac)) 2a.

Solution, a vaguely refers to the universal formula of the quadratic equation Qihong is calculated by the formula method, <>

Problem calculation process.

The universal formula for a quadratic equation is: ax2 + bx + c = 0. where a, b, and c are known numbers, and x is unknown.

The steps to solve a quadratic equation are as follows:

1.Calculate the discriminant δ =b2 - 4ac;

2.The case of judging the solution of the equation according to the value of the δ:

0 When you believe in it, the equation has two unequal real roots;

At 0, the equation has two equal real roots (one of which is x=-b 2a);

At 0, the equation has no real roots. Stove molding.

3.Solve according to the root finding formula:

When δ > 0, x = b 2a;

When δ > 0, x = b 2a;

4.The obtained root is substituted into the original equation to test whether the equation is satisfied.

The universal formula for the unary quadratic equation ax 2+bx+c=0 x=(-b (b 2-4ac)) 2a.

Solution: For the unary quadratic equation ax 2+bx+c=0(a≠0), it can be simplified to obtain x 2+b a*x+c a=0

x^2+2*b/2a*x+(b/a)^2-(b/2a)^2+c/a=0

x+b/2a)^2=(b/2a)^2-c/a

i.e. (x+b 2a) 2=(b 2-4ac) a 2

Then we can get x+b 2a= (b 2-4ac)) 2a, or x+b 2a=- (b 2-4ac)) 2a.

Then x=(-b+ (b 2-4ac)) 2a, or x=(-b- (b 2-4ac)) 2a.

So the universal solution formula for a quadratic equation is x=(-b (b 2-4ac)) 2a.