To solve a quadratic equation, you can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
A, b, and c are coefficients of the equation in the form of ax² + bx + c = 0. The quadratic formula provides two possible solutions for x, denoted by the ± symbol.
Now, let's take an example of a quadratic equation and solve it using the quadratic formula. Consider the equation:
2x² - 5x + 2 = 0
Here, a = 2, b = -5, and c = 2. Plugging these values into the quadratic formula gives:
x = (-(-5) ± √((-5)² - 4*2*2)) / 2*2
x = (5 ± √(25 - 16)) / 4
x = (5 ± √9) / 4
x = (5 ± 3) / 4
Therefore, the two possible solutions for x are:
x₁ = (5 + 3) / 4 = 8 / 4 = 2
x₂ = (5 - 3) / 4 = 2 / 4 = 0.5
To visualize this solution, we can plot the graph of the quadratic equation y = 2x² - 5x + 2. The graph will intersect the x-axis at x = 0.5 and x = 2, representing the two solutions we found using the quadratic formula.
Therefore, by using the quadratic formula and visual aids such as graphs, you can effectively solve quadratic equations and understand their solutions better.
