Quadratic Equation: Reflecting on Finding Solutions

What are the solutions of 2x^2 + 5x - 3 = 0?

A. x = 1, x = -3/2

B. x = 3, x = -1/2

C. x = 2, x = -3

D. x = 4, x = -3

Final answer:

The solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1 and x = -1.5.

Reflecting on the given quadratic equation 2x^2 + 5x - 3 = 0, we need to find the values of x that satisfy the equation when it equals zero. By using the quadratic formula (-b ± √(b^2 - 4ac)) / 2a, we can determine the solutions to this equation.

Solution Steps:

1. Identify a, b, and c from the equation ax^2 + bx + c = 0.

For 2x^2 + 5x - 3 = 0, a = 2, b = 5, and c = -3.

2. Substitute the values of a, b, and c into the quadratic formula.

Applying the formula, we have x = [-5 ± √(5^2 - 4*2*(-3))] / 2*2.

x = [-5 ± √(25 + 24)] / 4.

x = [-5 ± √49] / 4.

x = (-5 ± 7) / 4.

3. Calculate the solutions for x.

For x = (-5 + 7) / 4, we get x = 2 / 4, which simplifies to x = 0.5 (x = 1).

For x = (-5 - 7) / 4, we have x = -12 / 4, which simplifies to x = -3 (x = -1.5).

Therefore, the solutions to the quadratic equation 2x^2 + 5x - 3 = 0 are x = 1 and x = -1.5, matching option A.