To find the approximate solutions of the quadratic equation 2x² + 7x + 3 = 0, 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 first calculate the discriminant (b² – 4ac):
b² = (7)² = 49
4ac = 4 * 2 * 3 = 24
Discriminant = 49 – 24 = 25
Since the discriminant is positive, this means we have two real and distinct solutions. Now we can substitute the values of a, b, and the discriminant back into the quadratic formula.
Calculating the two possible values for x:
- x₁ = (-7 + √25) / (2 * 2)
- x₂ = (-7 – √25) / (2 * 2)
Calculating these:
- x₁ = (-7 + 5) / 4 = -2 / 4 = -0.5
- x₂ = (-7 – 5) / 4 = -12 / 4 = -3
Thus, the approximate solutions of the equation 2x² + 7x + 3 = 0, rounded to the nearest hundredth, are:
- x₁ ≈ -0.50
- x₂ ≈ -3.00
In conclusion, the solutions to the quadratic equation are approximately -0.50 and -3.00.