At Most Two Solutions

★ 8/10functions Quadratic Equations Absolute Value algebra Casework

Problem

Let $f(x) = -x^2 + bx + |x - a|$ with $a, b \in \mathbb{R}$ . Suppose that for every real $a$ , the equation $f(x) = a + 1$ has at most two distinct solutions. Find the range of possible values of the real number $b$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Quadratic Equations, Absolute Value, algebra, Casework

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.