How to Find the Solutions of Quadratic Equations
What is the formula to find the solutions of quadratic equations?
The quadratic equation is 2x² - 5x + 3 = 0. What are the solutions to this equation?
Formula to Find Solutions of Quadratic Equations:
The formula to find the solutions of quadratic equations is the quadratic formula:
Solutions to 2x² - 5x + 3 = 0:
The solutions to the equation 2x² - 5x + 3 = 0 are x = 1 and x = 1.5.
Quadratic equations are equations of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. To find the solutions of a quadratic equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where the discriminant, b² - 4ac, determines the nature of the solutions. If the discriminant is positive, the equation has two real solutions. If the discriminant is zero, the equation has one real solution. If the discriminant is negative, the equation has two complex solutions.
In the given example of the quadratic equation 2x² - 5x + 3 = 0, the solutions can be found by substituting the values of a, b, and c into the quadratic formula and solving for x:
x = (5 ± √(5² - 4*2*3)) / 4
x = (5 ± √(25 - 24)) / 4
x = (5 ± √1) / 4
x = (5 ± 1) / 4
Therefore, the solutions to the equation 2x² - 5x + 3 = 0 are x = 1 and x = 1.5.