5 Questions
What is the quadratic formula for solving the equation $ax^2 + bx + c = 0$?
$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
What is the discriminant of a quadratic equation $ax^2 + bx + c = 0$?
$b^2 - 4ac$
What is the solution to the quadratic equation $2x^2 - 5x + 2 = 0$ using the quadratic formula?
$x = 2, x = \frac{1}{2}$
When does the quadratic formula give imaginary roots for a quadratic equation?
When the discriminant is negative
What is the general form of a quadratic equation?
$ax^2 + bx + c = 0$
Study Notes
Quadratic Formula
- The quadratic formula is: x = (-b ± √(b^2 - 4ac)) / 2a
Discriminant of a Quadratic Equation
- The discriminant of a quadratic equation ax^2 + bx + c = 0 is b^2 - 4ac
Solution to a Quadratic Equation
- The solution to the quadratic equation 2x^2 - 5x + 2 = 0 using the quadratic formula is: x = (5 ± √(25 - 16)) / 4
- Simplifying the solution, we get: x = (5 ± √9) / 4, or x = (5 ± 3) / 4
Imaginary Roots
- The quadratic formula gives imaginary roots for a quadratic equation when the discriminant (b^2 - 4ac) is negative
General Form of a Quadratic Equation
- The general form of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0
Test your skills in solving quadratic equations using the quadratic formula with this intermediate algebra quiz. Practice applying the quadratic formula to find the solutions for various quadratic equations.
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