To find the approximate solutions of the quadratic equation 2x² + 9x + 8 = 0, we can apply the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / 2a
In our equation, the coefficients are:
- a = 2
- b = 9
- c = 8
Now, let’s calculate the discriminant (b² – 4ac):
- b² = 9² = 81
- 4ac = 4 * 2 * 8 = 64
- b² – 4ac = 81 – 64 = 17
The discriminant is positive (17), indicating that there are two real and distinct solutions. Now we can substitute the values into the quadratic formula:
x = (-9 ± √17) / (2 * 2)
Calculating the square root of 17:
- √17 ≈ 4.1231
Using this value, we now have:
- First solution: x₁ = (-9 + 4.1231) / 4 = -4.8769 / 4 ≈ -1.2192
- Second solution: x₂ = (-9 – 4.1231) / 4 = -13.1231 / 4 ≈ -3.2808
Now, rounding both solutions to the nearest hundredth:
- First solution: x₁ ≈ -1.22
- Second solution: x₂ ≈ -3.28
Thus, the approximate solutions of the equation 2x² + 9x + 8 = 0 to the nearest hundredth are:
- x₁ ≈ -1.22
- x₂ ≈ -3.28