Question

Write a quadratic equation such that the sum of its roots is 5 and the product of its roots is -11?

Answer 1

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.