ax²+bx+c=0
Answer:-
Free online quadratic formula calculator -Enter the Coefficient of a, b and c and then click the calculate button.
What is Quadratic Equations?
A quadratic equation is an algebraic equation of the second degree in one variable. It can be written in the form:
ax² + bx + c = 0
where a, b, and c are real numbers and a ≠ 0.
Example of the quadratic equation –
- 5x² + 10x + 6 = 0
- 2x² – 5x + 3 = 0
- 25x² + 65x – 7 = 0
Quadratic formula
The quadratic formula is a general formula for solving quadratic equations.
x = (-b ± √(b² – 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation.
b² – 4ac = Discriminant
The discriminant determines the nature of the roots:
| Discriminant | Nature of roots |
|---|---|
| b² – 4ac > 0 | Two distinct real roots |
| b² – 4ac = 0 | One real root (a repeated root or double root) |
| b² – 4ac < 0 | Two complex (conjugate) roots |
How to solve quadratic equations?
Problem: Solve the quadratic equation (2x^2 – 5x + 3 = 0).
Solved
- in this equation, a = 2, b = -5, c = 3
- Calculate the discriminant = b² – 4ac = (-5)² – 4*2*3 = 25 – 24 = 1
- Discriminant > 0, two real roots,
- First root, X1 = 5 + 1 / 4 = 3/2
- Second root, X2 = 5 -1 / 4 = 1
the roots of the quadratic equation are x1 = 3/2 and x2 = 1