Which of the following is a solution to the quadratic equation 2x2+5x=3

Question

? Assume that the solution has been rounded to the nearest hundredth, if applicable.(1 point)
Responses

x=1.2
x equals 1.2

x=0.25
x equals 0.25

x=−1.6
x equals negative 1.6

x=0.5

Answer 1

To solve the quadratic equation \( 2x^2 + 5x - 3 = 0 \), we can use the quadratic formula, which is given by:

\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \]

In your equation, \( a = 2 \), \( b = 5 \), and \( c = -3 \).

Now, let's calculate the discriminant \( b^2 - 4ac \):

\[ b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot (-3) = 25 + 24 = 49 \]

The discriminant is \( 49 \), which is positive, indicating that there are two real solutions.

Now substituting into the quadratic formula:

\[ x = \frac{{-5 \pm \sqrt{49}}}{2 \cdot 2} = \frac{{-5 \pm 7}}{4} \]

Calculating the two solutions:

1. For the positive root:

\[ x = \frac{{-5 + 7}}{4} = \frac{2}{4} = 0.5 \]

2. For the negative root:

\[ x = \frac{{-5 - 7}}{4} = \frac{{-12}}{4} = -3 \]

Thus, the solutions to the equation \( 2x^2 + 5x - 3 = 0 \) are \( x = 0.5 \) and \( x = -3 \).

Among the provided options, the answer is:

x = 0.5 (x equals 0.5)