Solving Quadratic Equations Using the Quadratic Formula – Practice Problems

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One way of solving quadratic equations of the form ax² + bx + c = 0 is by using the quadratic formula. The quadratic formula states that x = { [-b ± sqrt ( b² – 4ac)] / 2a] } , where a, b, and c are the coefficients of the quadratic equation (with a, b, and c being real numbers, and a ≠ 0).

For example, given the quadratic equation x² – 5x + 6 = 0, first identify the values of a, b, and c. The given equation has a = 1, b = -5, and c = 6. After identifying the values of a, b, and c, substitute these values into the quadratic formula. So, we get x = { 5 ± sqrt( (-5)² = 4(1)(6)) / 2(1)]}. Simplifying the formula by using PEMDAS, we get that x = 2 and 3. You can check if the solutions are correct by substituting them into the quadratic equation. Once they satisfy the equation or the result is true, then the solutions are correct.

Sometimes a quadratic equation has two solutions, exactly one solution, or has imaginary solutions. However, these solutions don’t always satisfy a given quadratic problem. These solutions are called extraneous solutions. Therefore, it is necessary to always check the solutions in order to get the correct one.

Solve quadratic equations in one variable.


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Exercises in this Practice Problem
Factor the quadratic equation.
Use the quadratic formula to solve the equation.
Find the value of $x$ which satisfies each quadratic equation.
Determine the path of the quadratic equation.
Identify the values of $a$, $b$, and $c$ for each quadratic equation.
Solve the given quadratic equations.