The quadratic equation is the equation of a type of ax^2+bx+c=0 (the sign "\designates by U-005E\" exponentiation, i.e. this case in the second). Somewhat there is a lot of types of the equation therefore to everyone the solution is required.
Instruction
1. Let there is ax^2+bx+c=0 equation, in it and, b, c – coefficients (any numbers), x – unknown number which needs to be found. The schedule of this equation is the parabola therefore to find roots of the equation is to find parabola points of intersection with an axis x. The quantity of points can be recognized by a discriminant. D=b^2-4ac. If this expression is more than zero, then two points of intersection; if it is equal to zero, then one; if it is less than zero, then there are no points of intersection.
2. And to find roots, it is necessary to substitute values in the equation: h1.2 = (-b+-Exp(D)) / (2a); (Exp () is a square root from number) Since the equation square, write h1 and h2, and find them as follows: for example, it is considered h1 in the equation with "+", and h2 with "-" (where "+ -"). Coordinates of top of a parabola are expressed by formulas: h0=-b/2a, u0= at (h0). If coefficient a> 0, branches of a parabola are directed up if and <0, down.
3. Example 1: Solve x^2+2*x–3=0 equation. Calculate a discriminant of this equation: D=2^2-4(-3)=16 Therefore, on a quadratic formula it is possible to receive at once, chtokh1.2= (-2+-Exp (16))/2=-1+-2x1=-1+2=1, х2=-1-2=-3Значит, x1=1, x2=-3 (two points of intersection with an axis x) the Answer. 1, −3.
4. Example 2: Solve x^2 equation +6*x+9=0. Calculating a discriminant of this equation, receive that D=0 and, therefore, this equation has one korenkh =-6/2=-3 (one point of intersection with an axis x) the Answer. x=–3.
5. Example 3: Solve the equation x^2+2*x +17=0. Calculate a discriminant of this equation: D=2^2–4*17=–64 <0. Therefore, this equation of the valid roots has no. (there are no points of intersection with an axis x) the Answer. There are no decisions.
6. There are still additional formulas which help at calculation of roots: (a+b) ^2=a^2+2ab+b^2 – a square of the sum (a-b) ^2=a^2-2ab+b^2 – a square разностиa^2-b^2=(a+b) (a-b) – the difference of squares