Question

Quadratic Equations Quick Check
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Question
Solve the equation 0=2x2−5x−3
algebraically using any method.(1 point)
Responses

x=−1
, x=32
x equals negative 1 , x equals Start Fraction 3 over 2 End Fraction

x=−12
, x=3
x equals negative Start Fraction 1 over 2 End Fraction , x equals 3

x=−32
, x=1
x equals negative Start Fraction 3 over 2 End Fraction , x equals 1

x=−3
, x=12

Answer 1

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

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

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

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

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

Now we can plug the values into the quadratic formula:

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

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

1. For \( 5 + 7 \):
\[
x = \frac{12}{4} = 3
\]

2. For \( 5 - 7 \):
\[
x = \frac{-2}{4} = -\frac{1}{2}
\]

Thus, the solutions are:

\[
x = 3 \quad \text{and} \quad x = -\frac{1}{2}
\]

So the correct response is:

**x=−12, x=3**
x equals negative Start Fraction 1 over 2 End Fraction, x equals 3