what are the steps in solving quadratics using the Quadratic Formula method?
arrange your quadratic in the form
ax^2+bx+c = 0
Then just plug the a,b,c values into the formula ...
To solve a quadratic equation using the Quadratic Formula, follow these steps:
1. Identify the coefficients a, b, and c of the quadratic equation in the general form: ax^2 + bx + c = 0. These coefficients will help us in plugging them into the Quadratic Formula.
2. Write down the Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a. This formula will allow us to find the values of x that satisfy the quadratic equation.
3. Plug the values of a, b, and c from the quadratic equation into the Quadratic Formula.
4. Simplify the expression inside the square root (√) in the formula by calculating b^2 - 4ac.
5. Determine whether the expression inside the square root is positive, negative, or zero. This step is crucial, as it will help us determine the nature of the solutions.
a. If the expression inside the square root is positive, then the quadratic equation has two distinct real solutions.
b. If the expression inside the square root is zero, then the quadratic equation has one real solution, often referred to as a "repeated root" or "double root."
c. If the expression inside the square root is negative, then the quadratic equation does not have any real solutions. Instead, it will have two complex conjugate solutions (involving the imaginary unit i).
6. Calculate the square root if the expression inside the square root is positive or zero.
7. Apply the "+" and "-" signs in the numerator of the formula and divide the result by 2a.
8. Write down the values of x, which will be the solutions to the quadratic equation.
By following these steps, you can effectively solve a quadratic equation using the Quadratic Formula method.
The steps involved in solving quadratic equations using the Quadratic Formula method are as follows:
Step 1: Write down the given quadratic equation in the standard form, which is: ax^2 + bx + c = 0. Ensure that the quadratic equation is set equal to zero.
Step 2: Identify the values of the coefficients a, b, and c.
Step 3: Substitute the values of a, b, and c into the quadratic formula, which is: x = (-b ± √(b^2 - 4ac)) / 2a.
Step 4: Simplify the inside of the square root, which is the discriminant (b^2 - 4ac).
Step 5: Determine the value of the discriminant to classify the nature of the solutions. If the discriminant is positive, there are two real roots. If the discriminant is zero, there is one real root (the solutions are repeated). If the discriminant is negative, there are no real roots (the solutions are complex conjugates).
Step 6: Calculate the value of the square root in the numerator of the quadratic formula.
Step 7: Add or subtract the numerator by the square root value, according to the ± sign in the quadratic formula.
Step 8: Divide the resulting expression by 2a.
Step 9: Simplify the expression to get the two solutions for the quadratic equation. If the discriminant is zero, the repeated solution will be obtained.
Step 10: Write down the solutions obtained as the final answer.