In the school program often it is necessary to face the solution of a quadratic equation of type: ax² + bx + c = 0, where and, b - the first and second coefficients of a quadratic equation, with - the free member. By means of value of a discriminant it is possible to understand whether is at the equation of the decision or not and if is, then how many.
Instruction
1. How to find a discriminant? There is a formula of its stay: D = b² - 4ac. At the same time, if D> 0, the equation has two valid roots which are calculated on formulas: x1 = (-b + VD) / 2a, x2 = (-b - VD) / 2a where V are meant by a square root.
2. To understand formulas in operation, solve several examples. Example: x \-12x + 35 = 0, in this case and = 1, b - (-12), and the free member with - + 35. Find a discriminant: D = (-12) ^2 - 4*1*35 = 144 - 140 = 4. Now find roots: X1 = (-(-12) + 2)/2*1 = 7, x2 = (-(-12) - 2)/2*1 = 5. At a> 0, x1 <x2, at a <0, x1> x2 that means if a discriminant more than zero: there are material roots, the schedule of square function crosses OX axis in two places.
3. If D = 0, then decision one: x = - b/2a. If the second coefficient of a quadratic equation of b represents even number, then it is expedient to find the discriminant divided on 4. At the same time the formula will take the following form: D/4 = b²/4 - ac. For example, 4x^2 - 20x + 25 = 0, where a = 4, b = (-20), with = 25. At the same time D = b² - 4ac = (20) ^2 - 4*4*25 = 400-400 = 0. The square trinomial has two equal roots, we will find them on formula x = - b/2a = - (-20)/2*4 = 20/8 = 2.5. If the discriminant is equal to zero, means there is one material root, the function graph crosses OX axis in one place. At the same time, if a> 0, the schedule is located above OX axis and if a <0, is lower than this axis.
4. At D <0 material roots do not exist. If the discriminant is less than zero, means there are no material roots but only complex roots, the function graph does not cross OX axis. Complex numbers - expansion of a set of real numbers. The complex number can be presented as the formal sum x + to iy where x and y - real numbers, i - imaginary unit.