quadratic formula
The quadratic formula is a mathematical formula used to find the roots or solutions of a quadratic equation
The quadratic formula is a mathematical formula used to find the roots or solutions of a quadratic equation. It is derived from completing the square method.
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where ‘a’, ‘b’, and ‘c’ are coefficients and ‘x’ represents the variable.
The quadratic formula states that the roots or solutions of a quadratic equation ax^2 + bx + c = 0 can be found using the formula:
x = (-b ± √(b^2 – 4ac)) / (2a)
Let’s break down the quadratic formula step by step:
1. Identify the coefficients: In the quadratic equation ax^2 + bx + c = 0, ‘a’, ‘b’, and ‘c’ represent coefficients. ‘a’ is the coefficient of the x^2 term, ‘b’ is the coefficient of the x term, and ‘c’ is the constant term.
2. Substitute the values into the formula: Replace ‘a’, ‘b’, and ‘c’ with their respective coefficients in the quadratic formula.
3. Simplify the expression under the square root: Calculate the value of the expression (b^2 – 4ac) inside the square root.
4. Evaluate the plus/minus: The quadratic formula has a plus-minus symbol (±) before the square root. This means that we need to calculate two possible solutions, one with a plus sign and one with a minus sign.
5. Divide by 2a: Now, divide the entire expression by 2a to obtain the values of ‘x’. Here, ‘2a’ refers to twice the coefficient of the x^2 term in the quadratic equation.
By following these steps, you can find the solutions for a quadratic equation using the quadratic formula. Remember that a quadratic equation can have two real solutions, one real solution, or no real solutions, depending on the discriminant (the expression inside the square root). If the discriminant is positive, there are two distinct real solutions. If it is zero, there is one real solution (a perfect square). If it is negative, there are no real solutions, but the equation has two complex solutions.
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