Determine the roots for the quadratic expression: x2 + x – 42 = 0?
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Answer: D. -7, 6
Explanation
Quadratic expressions can be factored into two binomial terms whose product equals zero. Finding two numbers that multiply to negative forty two and add to one gives positive six and negative seven. Setting each binomial factor to zero yields the exact equation roots of negative seven and six. Quadratic equations follow the standard polynomial form where factoring reveals the x intercept roots. The product of the roots equals the constant term, while their sum equals the negated linear coefficient. Zero product property states that if a product is zero, at least one factor must equal zero.
Physics projectile motion equations are quadratic functions whose roots determine landing times and distances. Engineering design calculations use quadratic roots to locate critical structural stress thresholds. Economic profit models analyze quadratic curves to find break even production quantities. Option A reverses the signs of the roots incorrectly leading to an invalid factoring solution. Option B uses incorrect integer factors that fail to multiply to negative forty two. Option C assigns incorrect values that do not satisfy the sum and product coefficient rules.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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