Question

Use the quadratic formula to solve 2x2+5x+3=0 .

Write your solutions as an integer and decimal rounded to the hundredths, if necessary.

(2 points)
x=

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Answer 1

To solve the quadratic equation \( 2x^2 + 5x + 3 = 0 \) using the quadratic formula, we first identify the coefficients \( a \), \( b \), and \( c \):

- \( a = 2 \)
- \( b = 5 \)
- \( c = 3 \)

The quadratic formula is:

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

Now we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = 5^2 - 4 \cdot 2 \cdot 3 = 25 - 24 = 1
\]

Now, applying the quadratic formula:

\[
x = \frac{{-5 \pm \sqrt{1}}}{{2 \cdot 2}} = \frac{{-5 \pm 1}}{4}
\]

Now we calculate the two possible values for \( x \):

1. Using the positive root:
\[
x_1 = \frac{{-5 + 1}}{4} = \frac{{-4}}{4} = -1
\]

2. Using the negative root:
\[
x_2 = \frac{{-5 - 1}}{4} = \frac{{-6}}{4} = -1.5
\]

Now, we write the solutions:

\[
x = -1 \quad \text{(integer)}
\]

\[
x = -1.5 \quad \text{(decimal rounded to the hundredths: -1.50)}
\]

So, the final answers are:

\[
x = -1
\]

\[
x = -1.50
\]