Question

Estimate the larger root of x² +x-1=0. Let x_(0)=1.

Answer 1

To estimate the larger root of the quadratic equation x² + x - 1 = 0, we can use the quadratic formula: x = (-b ± √(b² - 4ac)) / (2a). Plugging in the values, we find x ≈ (1 + √5) / 2.

Step-by-step explanation:

To estimate the larger root of the quadratic equation x² + x - 1 = 0, we can use the quadratic formula. The quadratic formula states that if we have an equation of the form ax² + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 1, b = 1, and c = -1. Plugging these values into the quadratic formula, we get:

x = (-1 ± √(1² - 4(1)(-1))) / (2(1))

Simplifying further, we have:

x = (-1 ± √(1 + 4)) / 2

x = (-1 ± √5) / 2

Since we are looking for the larger root, we take the positive value of √5:

x ≈ (1 + √5) / 2