Quadratic Equations
Quadratic Equations
star_batch_jee_advanced_2025
Grade 11
Question:
Given that $a > 0$, $|ax^2 + bx + c| \leq 1$ if $-1 \leq x \leq 1$, $a, b, c \in \mathbb{R}$ and $ax + b$ has its maximum value $2$ when $-1 \leq x \leq 1$. Then $c =$
Step-by-Step Solution
Key Concept: Function evaluations and extremum conditions provide redundant but consistent information to uniquely determine the quadratic.
Same solution structure as questions 13 and 14, deriving $a = 2$, $b = 0$, $c = -1$ from the given conditions on $f(0)$, $f(1)$, $f(-1)$ and optimization properties.
Correct Answer: 1