Final answer:
The roots of the equation 2x^2 + 9x - 5 = 0 are found using the quadratic formula. The two solutions are x = 0.5 and x = -5, which are calculated by substituting the coefficients into the quadratic formula and simplifying.
Step-by-step explanation:
The student is asking to find the two values of x that are roots of the quadratic equation 2x^2 + 9x - 5 = 0. To solve this, we can use the quadratic formula, which is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are coefficients from the equation of the form ax^2 + bx + c = 0. In the given equation, a = 2, b = 9, and c = -5. Substituting these values into the quadratic formula, we calculate the two possible solutions for x.
Here's how we apply the quadratic formula step by step:
1. First, calculate the discriminant: the part under the square root, b^2 - 4ac. That's 9^2 - 4(2)(-5), which is equal to 81 + 40 = 121.
2. Next, apply the discriminant to the formula: x = (-9 ± √121) / (2 * 2).
3. Since the square root of 121 is 11, we then have x = (-9 ± 11) / 4.
4. There are two solutions: for x = (-9 + 11) / 4, we have x = 2 / 4, which simplifies to x = 0.5, and for x = (-9 - 11) / 4, we get x = -20 / 4, which simplifies to x = -5.
Therefore, the roots of the equation 2x^2 + 9x - 5 = 0 are x = 0.5 and x = -5.