If 2x^2 + 3x - 5 = 0, what is the value of x using the quadratic formula?
Correct Answer: x = 1/2 or x = -5
- Step 1: Identify the coefficients a, b, and c from the equation 2x^2 + 3x - 5 = 0. Here, a = 2, b = 3, and c = -5.
- Step 2: Write down the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a.
- Step 3: Calculate b²: b² = 3² = 9.
- Step 4: Calculate 4ac: 4ac = 4 * 2 * (-5) = -40.
- Step 5: Calculate b² - 4ac: 9 - (-40) = 9 + 40 = 49.
- Step 6: Calculate the square root of (b² - 4ac): √49 = 7.
- Step 7: Substitute b, √(b² - 4ac), and a into the quadratic formula: x = [-3 ± 7] / (2 * 2).
- Step 8: Calculate the two possible values for x: x = [-3 + 7] / 4 and x = [-3 - 7] / 4.
- Step 9: Simplify the first value: x = 4 / 4 = 1.
- Step 10: Simplify the second value: x = -10 / 4 = -2.5.
- Step 11: The two possible values for x are 1 and -2.5.
- Quadratic Equations – Understanding how to solve quadratic equations using the quadratic formula.
- Quadratic Formula – Application of the formula x = [-b ± √(b² - 4ac)] / 2a to find the roots of a quadratic equation.
- Discriminant – Calculating the discriminant (b² - 4ac) to determine the nature of the roots.
