Final answer:
To solve the quadratic equation 2m² + 4m + 5 = 0 using the quadratic formula, we substitute the values of a = 2, b = 4, and c = 5 into the formula. Simplifying the equation, we find that the solutions for m involve imaginary numbers: m = -1 ± i√6. None of the option is correct
Step-by-step explanation:
We can solve the quadratic equation 2m² + 4m + 5 = 0 using the quadratic formula.
The quadratic formula states that if we have an equation of the form ax² + bx + c = 0, then the solutions for x can be found using the formula:
x = (-b ± √(b² - 4ac)) / 2a
For the given equation, a = 2, b = 4, and c = 5.
Plugging these values into the quadratic formula, we get:
m = (-4 ± √(4² - 4(2)(5))) / (2(2))
Simplifying further, we have:
m = (-4 ± √(16 - 40)) / 4
m = (-4 ± √(-24)) / 4
Since the discriminant (√(-24)) is negative, the solutions will involve imaginary numbers.
Therefore, the correct answer is:
m = -1 ± i√6
None of the option is correct