Final answer:
The roots of the equation 4K² + 8K + 5 = 10 are K = 0.5 and K = -2.5. This is found by rearranging the equation to standard form and applying the quadratic formula. The solution requires substituting the coefficients into the formula and solving for K.
Step-by-step explanation:
To describe the roots of the equation 4K² + 8K + 5 = 10, we first need to rearrange it to standard quadratic form, which means getting a 0 on one side. So the equation becomes 4K² + 8K - 5 = 0. We can then apply the quadratic formula, which states that the roots of a quadratic equation ax² + bx + c = 0 are given by (-b ± √(b² - 4ac)) / (2a).
In our equation, a = 4, b = 8, and c = -5. Plugging these values into the formula gives us:
Roots = (-8 ± √(8² - 4×4×(-5))) / (2×4)
Roots = (-8 ± √(64 + 80)) / 8
Roots = (-8 ± √144) / 8
Roots = (-8 ± 12) / 8
Thus, the roots of the equation 4K² + 8K + 5 = 10 are K = 0.5 and K = -2.5.