New Question: When solving a quadratic equation using the quadratic formula, what steps should be taken after finding the discriminant?
After finding the discriminant of a quadratic equation, the next steps to solve the equation using the quadratic formula are as follows:
1. Determine the value of the discriminant (denoted as Δ) by substituting the coefficients of the quadratic equation into the formula: Δ = b^2 - 4ac.
2. Based on the value of the discriminant:
a. If Δ > 0 (positive discriminant), the equation has two distinct real roots.
b. If Δ = 0 (zero discriminant), the equation has one real root (a perfect square trinomial).
c. If Δ < 0 (negative discriminant), the equation has no real roots (complex roots).
3. Once you know the nature of the roots, you can proceed with the quadratic formula, which is:
x = (-b ± √Δ) / 2a
Here, the ± symbol indicates that you will have two solutions, one with a positive sign (+) and the other with a negative sign (-).
4. Substitute the values of a, b, and Δ you obtained from the quadratic equation into the quadratic formula.
5. Simplify the expression by performing the necessary operations, such as addition, subtraction, multiplication, and division.
6. Calculate the values of x by evaluating the positive and negative solutions separately. This will give you the two possible solutions for the quadratic equation.
7. Express the final solutions in decimal or fraction form, depending on the given quadratic equation.
These steps will guide you in solving a quadratic equation using the quadratic formula after finding the discriminant.
After finding the discriminant of a quadratic equation, you can determine the nature of the roots and the number of solutions that the equation has. The discriminant, denoted as Δ, is calculated using the formula:
Δ = b^2 - 4ac
Here are the steps you should take after finding the discriminant:
1. If the discriminant is positive (Δ > 0), it means that the quadratic equation has two distinct real solutions. In this case, proceed to the next step.
2. If the discriminant is zero (Δ = 0), it means that the quadratic equation has one real solution, which is a repeated root. In this case, proceed to the next step.
3. If the discriminant is negative (Δ < 0), it means that the quadratic equation has no real solutions, but rather two complex conjugate solutions. In this case, the equation cannot be further simplified using real numbers.
After determining the nature of the roots based on the discriminant, you can use the quadratic formula to find the solutions of the equation:
x = (-b ± √Δ) / (2a)
In general, substitute the values of a, b, and c from the quadratic equation into the quadratic formula and simplify the expression. This will give you the values of x that satisfy the equation. The "±" symbol indicates that there are two possible solutions, either by adding or subtracting the square root of the discriminant.
Remember to simplify the equation further if possible and present the solutions in either decimal form or simplify them as fractions or radicals, depending on the given values.
I hope this helps! Let me know if you have any further questions.