If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is
Question
Solution 1
The given function f(x) is an even function because f(5 + x) = f(5 - x) for every real x. This means that the function is symmetric about the vertical line x = 5.
Given that f(x) = 0 has four distinct real roots, let's denote them as a, b, c, and d. Because of the symmetry, two of these roots will Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI
Similar Questions
If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is:(a) No real roots (b) 2 equal real roots(c) 2 distinct real roots (d) More than 2 real roots
f one of the two roots of x²- 4x - k = 0 is twice the other roots, then find the value of k.
If the roots of equation 𝑥2 − 6𝑥 + 𝑘 = 0 are real and distinct, then value of k is:(a) > –9(b) > –6(c) < 6(d) < 9
Let equation x3 – 9x2 + 24x + λ = 0 has three real and distinct roots a, b, c. If λ ∈ (–20, –18), then the value of ([a] + [b] + [c]) will be
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.