Let f(x) be a quadratic polynomial in x such that f(x)≥0 for all real numbers x. If f(2)=0 and f(4)=6, then f(-2) is equal to
Question:
Let f(x) be a quadratic polynomial in x such that f(x)≥0 for all real numbers x. If f(2)=0 and f(4)=6, then f(-2) is equal to
Let f(x) be a quadratic polynomial in x such that f(x)≥0 for all real numbers x. If f(2)=0 and f(4)=6, then f(-2) is equal to
Options
Answer: (3) 24
Explanation:
Since f(x)≥0 and f(2)=0, we have f(x)=a(x-2)². Using f(4)=6: a(4-2)²=6, so 4a=6, giving a=3/2. Therefore f(x)=3/2(x-2)² and f(-2)=3/2(-2-2)²=3/2×16=24.
Explanation:
Since f(x)≥0 and f(2)=0, we have f(x)=a(x-2)². Using f(4)=6: a(4-2)²=6, so 4a=6, giving a=3/2. Therefore f(x)=3/2(x-2)² and f(-2)=3/2(-2-2)²=3/2×16=24.
👉 Want AI explanation? Open in MCQ App
Recommended articles
- How To Cover Current Affairs For Upsc Prelims — Master UPSC Current Affairs with daily newspaper reading, Vision IAS monthly compilations, PT 365, and MCQ practice. Complete strategy guide for Prelims…
- Top 10 Daily Current Affairs Resources For Upsc Aspirants — Discover the best daily current affairs resources for UPSC 2026. Complete guide with The Hindu, PIB, Sansad TV, and 7 more proven sources. Expert…
- Free Cat Previous Year Questions Guide — Master CAT 2025 with free previous year questions. Practice 1000+ PYQs, mock tests, and detailed solutions. Complete guide to CAT preparation using past…