Question

If the solution set of a quadratic equation is the square root of 5 and -5 where the leading coefficient is 2, find the quadratic equation.

Answer 1

The quadratic equation with solutions square root of 5 and -5 and a leading coefficient of 2 is 2x² - 10 = 0.

Step-by-step explanation:

To find the quadratic equation with solutions square root of 5 and -5, and a leading coefficient of 2, we use the fact that the solutions (or roots) of a quadratic equation can be plugged into the formula ax² + bx + c = 0.

Let √5 (the square root of 5) be r1 and -√5 (negative square root of 5) be r2. The quadratic equation can be constructed from these roots as follows:

1. The standard form of a quadratic equation is ax² + bx + c = 0.
2. Since the leading coefficient is 2, the equation will be in the form of 2x² + bx + c = 0.
3. Using the fact that the solutions to a quadratic equation are given by (x - r1)(x - r2) = 0, we have (x - √5)(x + √5) = 0.
4. Expanding the product, we obtain x² - (√5)² = x² - 5.
5. To include the leading coefficient of 2, we multiply by 2 to get 2x² - 10.

Therefore, the quadratic equation with the given solutions and leading coefficient is 2x² - 10 = 0.