For the solution of a quadratic equation and finding of its smallest root the discriminant is calculated. The discriminant will be equal to zero only in case the polynomial has multiple roots.
It is required to you
- - mathematical reference book;
- - calculator.
Instruction
1. Lead a polynomial to a quadratic equation of a type of ax2 + bx + c = 0 in which a, b and c are any real numbers, at this a 0 should not equal at all.
2. Substitute values of the turned-out quadratic equation in a formula for calculation of a discriminant. This formula looks as follows: D = b2 - 4ac. In case the D more than zero, a quadratic equation has two roots. If D equals to zero, both calculated a root will be not only material, but also equal. And the third option: if the D less than zero, roots represent complex numbers. Calculate value of roots: h1 = (-b + sqrt (D)) / 2a and h2 = (-b - sqrt (D)) / 2a.
3. For calculation of roots of a quadratic equation you can use also following formulas: h1 = (-b + sqrt (b2 - 4ac)) / 2a and h2 = (-b - sqrt (b2 - 4ac)) / 2a.
4. Compare two calculated roots: the root with the smallest value also is required you size.
5. Without knowing roots of a square trinomial, you with ease can find their sum and the work. For this purpose use Vieta theorem according to which the sum of roots of the square trinomial presented in the form by x2 + px + q = 0 equals to the second coefficient, that is p, but with the opposite sign. member of q. In other words, x1 + x2 = – p, and x1x2 = q. For example, the following quadratic equation is given: x \-5x + 6 = 0. For a start spread out 6 to two multipliers and so that the sum of these multipliers was equal to 5. If you picked up values correctly, then x1 = 2, x2 = 3. Check yourself: 3x2=6, 3+2=5 (as well as it is required, 5 with the opposite sign, that is "plus").