How to solve equations of degree
The solution of the degrees included in the school curriculum, and in high school. To learn how to solve these equations, it is necessary to be able to classify them, and depending on their type, apply a specific algorithm.
You will need:
- notebook; - a pen
Instruction how to solve equations of degree
Determine what species include the degree of the equation. It can be square or biquadratic, and equation with odd powers. Pay attention to the highest degree. If it is the second - the equation of the square, if the first - linear. If a higher degree of the equation is the fourth, and is the coefficient and variable in the second degree, the equation is biquadratic.
Notice the structure of the equation. If it has two terms, which are variable in some degree and the coefficient of the equation is solved quite simply: insert a variable in one part of the equation, as the numerical value of the other. Extract from the root of the extent to which there is a variable. If the degree is odd, we can immediately write down the answer if even, the equation has two solutions - the counted number, and it is the same, only with the opposite sign.
Note that the quadratic equation has the form: a * x ^ 2 + b * x + c = 0. Calculate the discriminant of the equation, using the formula: D = b * b-4 * a * c. Pay attention to get back sign. If the discriminant is less than zero, the equation has no solution. If the discriminant is zero or greater than zero, consider the well-known formula of roots of the equation: x = (-b-root (D)) / (2 * a).
To solve biquadratic equation of the form: a * x ^ 4 + b * x ^ 2 + c = 0, use the replacement x ^ 2 = y, and solve biquadratic equation as a square. As a result, in this case, you get two y, go back to the x ^ 2. That is, the two forms of the equation of the form x ^ 2 = a. To solve such an equation, use the instructions above.
If the equations are odd powers, try to bring them to the equations, having even powers. For this equation to a variable divide either one or several times. If it does not contain factors include the number of roots 0.