To find the approximate solutions of the quadratic equation 2x² + 7x + 3, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a = 2, b = 7, and c = 3. Let’s substitute these values into the formula:
x = (-(7) ± √((7)² – 4(2)(3))) / (2(2))
First, we need to calculate the discriminant:
b² – 4ac = 7² – 4(2)(3) = 49 – 24 = 25
Now we can substitute the value of the discriminant back into the quadratic formula:
x = (-7 ± √25) / 4
Since the square root of 25 is 5, we have:
x = (-7 ± 5) / 4
This gives us two potential solutions:
x₁ = (-7 + 5) / 4 = -2 / 4 = -0.5
x₂ = (-7 – 5) / 4 = -12 / 4 = -3
Now, rounding these solutions to the nearest hundredth:
- -0.5 remains -0.50
- -3 remains -3.00
Therefore, the approximate solutions of the equation 2x² + 7x + 3 rounded to the nearest hundredth are:
-0.50 and -3.00.