Advice 1: How to find the root of the equation

The equation is called equality of the form f(x,y,...)=g(x,y,..) where f and g are functions of one or several variables. To find the root of an equation means finding the set of arguments at which this equality occurs.
How to find the root of the equation
You will need
  • Knowledge in mathematical analysis.
Instruction
1
Let's say you have an equation of the form: x+2=x/5. For starters, move all components of this equality from the right side to the left, changing the sign of the component on the opposite. In the right part of this equation will be zero, i.e., we get the following: x+2-x/5 = 0.
2
We give similar terms. Will receive the following: 4x/5 + 2 = 0.
3
Further, from the obtained equation, we find the unknown addend, which in this case is X. the resulting value of the unknown variable will be the solution to the original equation. In this case, we get the following: x = -2,5.
Note
The solutions may be extra roots. They will not be the solution to the original equation, even if you do all correctly decided. Be sure to check all of the solution.
Useful advice
The obtained values of the unknown always check. It's easy to do, substituting the obtained value in the original equation. If the equality is true, then the decision is correct.

Advice 2 : How to find the smallest root

For the solution of the quadratic equation and find the smallest root discriminant is calculated. The discriminant is equal to zero only if the polynomial has multiple roots.
How to find the smallest root
You will need
  • mathematical Handbook;
  • calculator.
Instruction
1
Bring the polynomial to a square equation of the form ax2 + bx + c = 0 where a, b and c are arbitrary real numbers, with a in no case must not equal 0.
2
Substitute the values of the resulting quadratic equation into the formula for calculating the discriminant. This formula is as follows: D = b2 - 4ac. In that case, if D is greater than zero, the quadratic equation will have two roots. If D equals zero, both the calculated root, will be not only real, but equal. Third option: if D is less than zero, the roots will be a complex number. Calculate the value of the roots: x1 = (-b + sqrt (D)) / 2a and x2 = (-b - sqrt (D)) / 2a.
3
To calculate roots of a quadratic equation can also use the following formula: x1 = (-b + sqrt (b2 - 4ac)) / 2a and x2 = (-b - sqrt (b2 - 4ac)) / 2a.
4
Compare the two calculated root: root with the smallest value is the desired value you.
5
Not knowing the roots of a quadratic trinomial, you can easily find their sum and product. Use the vieta theorem, according to which the sum of the square roots of the trinomial represented in the form x2 + px + q = 0, is equal to the second ratio, that is, p, but with opposite sign. The product of the roots corresponds to the value of the free term q. In other words, x1 + x2 = – p, and x1x2 = q. For example, given the following quadratic equation: x2 – 5x + 6 = 0. To start, lay 6, two multiplier, and so that the sum of these multipliers was equal to 5. If you picked up the values correctly, then x1 = 2, x2 = 3. Test yourself: 3x2=6, 3+2=5 (as required, 5 with the opposite sign, i.e. "plus").
Note
Be careful not to make a mistake, placing signs!
Useful advice
The number with the sign "minus" is always less than positive. If I compare two negative values, then less of them will be the fact that the module is more.
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