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Home » But problem implies integer exists. Recheck: perhaps typo in setup? - Crankk.io

But problem implies integer exists. Recheck: perhaps typo in setup? - Crankk.io

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Area \( = ext{length} imes ext{width} = 16 imes 8 = 128 \).

📌 A quadratic equation \( ax^2 + bx + c = 0 \) has roots 3 and -2. If \( a = 1 \), find \( b \) and \( c \), and determine the value of the expression \( b^2 - 4ac \).

📌 Using Vieta's formulas:

📌 Sum of roots \( = -rac{b}{a} = 3 + (-2) = 1 \).

📌 Product of roots \( = rac{c}{a} = 3 imes (-2) = -6 \).

📌 Therefore, \( b = -1 \) and \( c = -6 \).

📌 The expression is \( b^2 - 4ac = (-1)^2 - 4(1)(-6) = 1 + 24 = 25 \).

📌 \( S_{n-1} = 3(n-1)^2 + 5(n-1) = 3(n^2 - 2n + 1) + 5n - 5 = 3n^2 - 6n + 3 + 5n - 5 \)

🔥 Popular Posts

Try $ m = 2 $: $ x = 78 $
Both 43 and 78 are two-digit numbers satisfying the conditions.
Thus, the possible answers are $ \boxed{43} $ and $ \boxed{78} $.
Question: What is the largest integer that must divide the product of...
Solution: Let the four consecutive integers be $ n, n+1, n+2, n+3 $. T...
We analyze divisibility properties:
Among any four consecutive integers, at least one is divisible by 4.
At least two are even, so the product is divisible by $ 2 \cdot 2 = 4...
At least one is divisible by 3.
Therefore, the product is divisible by $ 4 \cdot 2 \cdot 3 = 24 $.

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