1) Solve

Question

2x2−5x−3=0and enter solutions below.

2) Push the "Graph It" Button to see a graph of
y=2x2−5x−3

Solution 1:

Solution 2:

Answer 1

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

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

Here, \( a = 2 \), \( b = -5 \), and \( c = -3 \).

1. First, calculate the discriminant \( b^2 - 4ac \):

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

2. Now use the quadratic formula:

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

3. This gives us two solutions:

• For the positive case:

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

• For the negative case:

\[ x = \frac{5 - 7}{4} = \frac{-2}{4} = -\frac{1}{2} \]

So, the solutions are:

Solution 1: \( x = 3 \)

Solution 2: \( x = -\frac{1}{2} \)

You might want to enter these solutions in the provided format.