Solve the equation: 2 x squared minus 5 x plus 1 equals 0.

Question

(1 point)
Responses

x equals start fraction 5 plus or minus start root 17 end root over 2 end fraction
Image with alt text: x equals start fraction 5 plus or minus start root 17 end root over 2 end fraction

x equals start fraction 5 plus or minus start root 17 end root over 4 end fraction
Image with alt text: x equals start fraction 5 plus or minus start root 17 end root over 4 end fraction

x equals start fraction negative 5 plus or minus start root 17 end root over 4 end fraction
Image with alt text: x equals start fraction negative 5 plus or minus start root 17 end root over 4 end fraction

x equals start fraction 5 plus or minus start root 21 end root over 4 end fraction

Answer 1

To solve the quadratic equation \(2x^2 - 5x + 1 = 0\), we can use the quadratic formula:

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

where \(a = 2\), \(b = -5\), and \(c = 1\).

1. Calculate the discriminant \(b^2 - 4ac\): \[ b^2 = (-5)^2 = 25 \] \[ 4ac = 4 \cdot 2 \cdot 1 = 8 \] \[ b^2 - 4ac = 25 - 8 = 17 \]

2. Substitute into the quadratic formula: \[ x = \frac{-(-5) \pm \sqrt{17}}{2 \cdot 2} \]

3. Simplify: \[ x = \frac{5 \pm \sqrt{17}}{4} \]

Thus, the solutions to the equation \(2x^2 - 5x + 1 = 0\) are:

\[ x = \frac{5 \pm \sqrt{17}}{4} \]

The correct response is:

x equals start fraction 5 plus or minus start root 17 end root over 4 end fraction.