Let α and β be the roots of the quadratic equation x² − 2bx + c² = 0 where b, c are positive real numbers. Let A be the arithmetic mean of α and β; and G be the geometric mean of α and β. What are the roots of the quadratic equation x² − (b + c) x + bc = 0?

Question

Accepted Answer

A, G. From x² − 2bx + c² = 0: α + β = 2b and αβ = c². So A = (α+β)/2 = b and G = √(αβ) = c. The equation x² − (b+c)x + bc = 0 factors as (x − b)(x − c) = 0, giving roots b and c, which equal A and G respectively.

Let α and β be the roots of the quadratic equation x² − 2bx + c² = 0 where b, c are positive real numbers. Let A be the arithmetic mean of α and β; and G be the geometric mean of α and β. What are the roots of the quadratic equation x² − (b + c) x + bc = 0?

Explanation

More Quadratic Equations questions

Want more NDA practice?