how to find roots in quadratic equation how to find roots in quadratic equation ​

Answer:To find the roots of a quadratic equation (an equation of the form ax² + bx + c = 0), you can use the quadratic formula: x = (-b ± √(b² - 4ac)) / 2a. The ± sign indicates there will be two potential roots, one found with the plus and the other with the minus. Step-by-step explanation:1. Identify a, b, and c:In the quadratic equation ax² + bx + c = 0, a, b, and c are the coefficients. For example, in the equation 2x² + 5x - 3 = 0, a = 2, b = 5, and c = -3.2. Calculate the discriminant (b² - 4ac):The discriminant (often represented by the symbol Δ or D) helps determine the nature of the roots.3. Apply the quadratic formula:Plug the values of a, b, and the discriminant into the formula: x = (-b ± √(b² - 4ac)) / 2a.4. Simplify:Calculate the two possible values of x, one with the plus sign and one with the minus. These are your roots.Example:Let's find the roots of the equation x² - 3x - 4 = 0. a = 1, b = -3, and c = -4 The discriminant is (-3)² - 4 * 1 * (-4) = 9 + 16 = 25 x = (3 ± √25) / (2 * 1)x = (3 + 5) / 2 = 4 or x = (3 - 5) / 2 = -1So, the roots of the equation x² - 3x - 4 = 0 are 4 and -1. Alternative Methods:While the quadratic formula is reliable, you can also find roots using: Factoring:If the quadratic expression can be factored, set each factor to zero and solve for x.Completing the square:A method that transforms the equation into a perfect square, making it easier to solve.Graphing:The roots are the x-intercepts of the parabola represented by the quadratic equation.hope it helps you bye bye

Answered by mojadocarmencito37 | 2025-07-05