How to solve the equation of the square root
Quadratic equation - the equation of the form ax ^ 2 + bx + c = 0 (the sign "*" denotes exponentiation, ie in this case the second). Species equation quite a lot, so everyone needs their decision.
Instruction how to solve the equation of the square root
Let the equation of ax ^ 2 + bx + c = 0, and in it, b, c - coefficients (any number), x - an unknown number that you want to find. The graph of this equation is a parabola, so finding the roots of the equation - is to find the point of intersection of the parabola with the x axis. The number of points can be identified by the discriminant. D = b ^ 2-4ac. If this expression is greater than zero, the two intersection points; if it is zero, one; if less than zero, then no intersection points.
And in order to find the roots themselves, substitute the values in equation h1,2 = (-b + -Exp (D)) / (2a); (Exp () - the square root of the number) Because quadratic equation, then we write x1 and x2, and find them as follows: for example, is considered to x1 in the equation with the "+" and x2 with the "-" (where "+ -"). The coordinates of the vertex of the parabola are given by x0 = -b / 2a, y0 = y (x0). If agt coefficient; 0, a parabola branch directed upwards, and if
Example 1: Solve the equation x ^ 2 + 2 * x-3 = 0. Calculate this discriminant equation: D = 2 ^ 2-4 (-3) = 16 Consequently, according to the formula of the roots of the quadratic equation can be obtained directly that h1,2 = (- 2 + -Exp (16)) / 2 = -1 + -1 x1 = -2 + 2 = 1, x2 = -3 = -1-2 Hence, x1 = 1, x2 = -3 (with two points of intersection of x-axis) response. 1 -3.
Example 2: Solve the equation x ^ 2 + 6 * x + 0 = 9. Evaluating the discriminant of this equation, we get that D = 0, and therefore, this equation has one root x = -6/2 = -3 (one with the x-axis crossing point) A. x = -3.
Example 3: Solve equation x ^ 2 + 2 * x + 0 = 17. Calculate the discriminant of the equation: D = 2 ^ 2-4 * 17 = -64 lt; 0. Therefore, the equation has real roots. (Intersection with the x axis points not) answer. There is no solution.
There are still additional formulas that help in calculating the roots of: (a + b) ^ 2 = a ^ 2 + 2ab + b ^ 2 - the square of the sum of (ab) ^ 2 = a ^ 2-2ab + b ^ 2 - the square of a difference ^ 2-b ^ 2 = (a + b) (ab) - the difference of squares