Therefore, discriminant > 0 the roots are real and different. Note: Please refer to the table at the beginning to see the corresponding formula.įor example: Let us consider the equation: 6x² + 11x - 35 = 0. We will compare the calculated discriminant with each of the conditions and whichever is satisfied, we will calculate the two roots by the corresponding formula and then display it. If the discriminant is less than 0, then the roots are imaginary and different. If the discriminant is equal to 0, then the roots are real and equal. If yes, then the roots of the equation are real and different. We will now check whether the discriminant is greater than 0. Example x2 + x - 6 0 The equation factorises to give (. Determine the value of k for which the quadratic expression (x-k) (x-10) +1 0 has integral roots. Finding roots by factorising If a quadratic equation can be factorised, the factors can be used to find the roots of the equation. After that the discriminant is calculated by the given formula. Hence, the roots of a quadratic equation are real, unequal, and irrational. Else if discriminant < 0 then, there are two distinct complex roots where root1 -b / (2a) and root2 -b / (2a). If discriminant 0 then, root1 root2 -b / (2a). Learn - Program to find square root of a number using sqrt () function.

The algorithm starts off by taking the coefficients of the equation, a, b and c from the user. root1 (-b + sqrt (discriminant)) / (2a) and root2 (-b - sqrt (discriminant)) / (2a). Calculate discriminant = (b * b) – (4 * a * c)Ĥ.1: Calculate root1 = ( -b + sqrt(discriminant)) / (2 * a)Ĥ.2: Calculate root2 = ( -b - sqrt(discriminant)) / (2 * a)Ĥ.3: Display “Roots are real and different”Ħ.2:Calculate imaginary = sqrt(-discriminant) / (2 * a) Read the coefficients of the equation, a, b and c from the user. Note that the quadratic formula actually has many real-world applications, such as calculating areas, projectile trajectories, and speed, among others.Step 2. This is demonstrated by the graph provided below. Furthermore, the quadratic formula also provides the axis of symmetry of the parabola. The x values found through the quadratic formula are roots of the quadratic equation that represent the x values where any parabola crosses the x-axis. Recall that the ± exists as a function of computing a square root, making both positive and negative roots solutions of the quadratic equation. Below is the quadratic formula, as well as its derivation.įrom this point, it is possible to complete the square using the relationship that:Ĭontinuing the derivation using this relationship: Only the use of the quadratic formula, as well as the basics of completing the square, will be discussed here (since the derivation of the formula involves completing the square). A quadratic equation can be solved in multiple ways, including factoring, using the quadratic formula, completing the square, or graphing. For example, a cannot be 0, or the equation would be linear rather than quadratic.

The numerals a, b, and c are coefficients of the equation, and they represent known numbers. Where x is an unknown, a is referred to as the quadratic coefficient, b the linear coefficient, and c the constant. In algebra, a quadratic equation is any polynomial equation of the second degree with the following form:

lets take a look at the graph of a quadratic function, and define a few new vocabulary words that are associated with. A quadratic function is always written as: f (x) ax2 + bx + c. Fractional values such as 3/4 can be used. Since y mx + b is an equation of degree one, the quadratic function, y ax2 + bx + c represents the next level of algebraic complexity.

Roots of quadratic equation