Final Answer:
The quadratic equation with sum of roots as 5 and product of roots as -11 is given by:
x² + (5 ± √249) / 2 * x - 11 / 4 = 0.
Step-by-step explanation:
Let the roots of the quadratic equation be x₁ and x₂.
According to the given conditions, we have:
x₁ + x₂ = 5 (sum of roots)
x₁ * x₂ = -11 (product of roots)
Now, let's substitute the values in the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Here, a = 1 (coefficient of x²), b = -5 (coefficient of x), and c = -11 (constant term).
Substituting these values in the quadratic formula, we get:
x = (-(-5) ± √((-5)² - 4(1)(-11))) / 2(1)
Simplifying, we get:
x = (5 ± √(25 + 224)) / 2
x = (5 ± √249) / 2
Therefore, the quadratic equation with the given conditions is:
x² + (5 ± √249) / 2 * x - 11 / 4 = 0.