Draw the flowchart for finding the roots of quadratic equation. Write the program for same….Pseudo Code Algorithm:

1. Start.
2. Input a, b, c.
3. D ← sqrt (b × b – 4 × a × c).
4. X1 ← (-b + d) / (2 × a).
5. X2 ← (-b – d) / (2 × a).
6. Print x1, x2.
7. Stop.

The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

The roots of any quadratic equation is given by: x = [-b +/- sqrt(-b^2 – 4ac)]/2a. Write down the quadratic in the form of ax^2 + bx + c = 0. If the equation is in the form y = ax^2 + bx +c, simply replace the y with 0. This is done because the roots of the equation are the values where the y axis is equal to 0.

Quadratic equations are the polynomial equations of degree 2 in one variable of type: f(x) = ax2+ bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x). A quadratic equation will always have two roots.

A flowchart is a type of diagram that represents a workflow or process. A flowchart can also be defined as a diagrammatic representation of an algorithm, a step-by-step approach to solving a task. The flowchart shows the steps as boxes of various kinds, and their order by connecting the boxes with arrows.

The Flowchart is the most widely used graphical representation of an algorithm and procedural design workflows. It uses various symbols to show the operations and decisions to be followed in a program. It flows in sequential order.

Hence, the correct answer is x2 – 8x + 15 = 0.

There are three types of roots of a quadratic equation ax2+bx+c=0 a x 2 + b x + c = 0 : Real and distinct roots. Real and equal roots. Complex roots.

The formula to find the roots of the quadratic equation is x = −b±√b2−4ac2a − b ± b 2 − 4 a c 2 a . The sum of the roots of a quadratic equation is α + β = -b/a = – Coefficient of x/ Coefficient of x2. The quadratic equation having roots α, β, is x2 – (α + β)x + αβ = 0.

A quadratic equation will always have two roots. The nature of roots may be either real or imaginary. The general form of quadratic equation: ax 2 + bx + c Example: 4x 2 + 6x + 12

Quadratic equations are the polynomial equations of degree 2 in one variable of type: f (x) = ax 2 + bx + c where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where ‘a’ is called the leading coefficient and ‘c’ is called the absolute term of f (x).

The term b 2 – 4ac is known as the discriminant of a quadratic equation. It tells the nature of the roots. We are going to use the above logic to solve this problem. Let us take a look at the algorithm and flowchart to have a better understanding.

If a = 0, then the equation is linear, not quadratic. The constants a, b, and c are called, respectively, the quadratic coefficient, the linear coefficient and the constant or free term. Because the quadratic equation involves only one unknown, it is called “univariate”.