If the value of D is positive, the roots obtained are real and unequal, and when D is negative, then roots are complex conjugates, so there are no real roots.įactorization and completing the square method are two other ways to solve a quadratic equation. When the value of D is zero, the roots are said to be real and equal. The nature of the roots obtained from the quadratic formula is decided by the discriminant (D), which is given as:
On a graph, for any parabola which is described as y = ax 2 +bx+c, the roots are the points (or values), where the parabola crosses the x-axis. The discriminant is important because it tells you how many roots a quadratic function has. The term b 2 −4 ac is called the discriminant. When we do this, we arrive at the quadratic formula, which is given as:īy solving the above equation, the value of x (root) is determined, and the sum of the roots and product of the roots of the equation can also be derived further. To find the roots of a quadratic function, we can set f ( x) = 0, and solve the equation, by completing the square. The quadratic equation is generally given as: Therefore, a quadratic function may have one, two, or zero roots.
It is often tricky to factorize some specific types of quadratic equations however, the roots (also called x-intercepts or zeros) of such equations can be easily calculated using the quadratic formula. A quadratic function is graphically represented by a parabola with vertex located at the origin, below the x-axis, or above the x-axis.
0 kommentar(er)
