Questions: 2x^2+16x+1=0

Solution Steps

To solve the quadratic equation \(2x^2 + 16x + 1 = 0\), we can use the quadratic formula, which is given by \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). Here, \(a = 2\), \(b = 16\), and \(c = 1\). We will calculate the discriminant \(b^2 - 4ac\) to determine the nature of the roots and then apply the formula to find the solutions.

For the quadratic equation \(2x^2 + 16x + 1 = 0\), we identify the coefficients as follows:

• \(a = 2\)
• \(b = 16\)
• \(c = 1\)

The discriminant \(D\) is calculated using the formula: \[ D = b^2 - 4ac \] Substituting the values: \[ D = 16^2 - 4 \cdot 2 \cdot 1 = 256 - 8 = 248 \]

The roots of the equation can be found using the quadratic formula: \[ x = \frac{-b \pm \sqrt{D}}{2a} \] Substituting the values: \[ x = \frac{-16 \pm \sqrt{248}}{2 \cdot 2} \] Calculating the roots: \[ x_1 = \frac{-16 + \sqrt{248}}{4} \approx -0.0630 \] \[ x_2 = \frac{-16 - \sqrt{248}}{4} \approx -7.9370 \]

Final Answer