Solve equations I. x2 + 3x – 18 = 0 and II. y2 + y – 30 = 0 to determine x and y?
Show answer Hide answer
Answer: E. If x = y or the relationship between x and y cannot be established.
Explanation
Quadratic equation roots can overlap across different intervals on the number line. Solving the first equation gives specific roots that intersect the roots of the second. An overlapping range prevents establishing a definitive and consistent inequality between variables. Quadratic equations typically yield two distinct real or imaginary roots upon solving. Factoring x squared plus 3x minus 18 equals zero yields roots negative six and three. Factoring y squared plus y minus 30 equals zero yields roots negative six and five.
Comparative analysis of inequalities is common in competitive examinations and data screening. Determining variable relationships helps analysts identify trends in multivariate datasets. Overlapping intervals frequently occur in statistical range comparisons. Claiming x is always less than y ignores the overlapping root values completely. Claiming x is always greater than y contradicts the shared negative root values. Claiming a strict equality ignores the distinct multiple root values present.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. p exceeds q by 50%. Express the ratio of p to q.
Show answer Hide answer
Answer: A. 3:2
An increase of fifty percent means the larger quantity equals one hundred fifty percent of the smaller baseline quantity. Expressing this relationship mathematically gives the equation p equals one point five times q, si...
Q2. Selling an item for Rs. 425 yields a profit equal to the loss incurred from selling it at Rs. 355. The item's cost is:________?
Show answer Hide answer
Answer: B. Rs. 390
The correct answer is three hundred ninety rupees for the item cost price. The profit made at four hundred twenty-five equals the loss incurred at three hundred fifty-five. Averaging the two selling prices finds the exac...
Q3. In a 1000 m event, A defeats B by 100 m, whereas in an 800 m event, B defeats C by 100 m. By what margin will A defeat C in a 600 m event?
Show answer Hide answer
Answer: B. 127.5 m
A defeats B by one hundred meters in a one thousand meter race, establishing a speed ratio. B defeats C by one hundred meters in an eight hundred meter race, establishing another speed ratio. Combining these proportional...
Q4. If X covers 48m while Y covers 42m, by what distance does X defeat Y in a 1km race:_________?
Show answer Hide answer
Answer: B. 125m
The problem establishes a constant proportional rate of movement between the two runners over any given distance. Using the given distances, Y covers forty-two meters for every forty-eight meters that X successfully cove...
Q5. Solve equations I. x2 – x – 42 = 0 and II. y2 – 17y + 72 = 0 to determine x and y?
Show answer Hide answer
Answer: A. If x < y
The correct answer is x is less than y because all x roots are smaller than y roots. Solving equation one yields roots of positive seven and negative six. Solving equation two yields roots of positive eight and positive...
Q6. Rajan borrowed Rs. 4000 at 5% p.a. compound interest, paid Rs. 2210 after 2 years, and settled the rest 2 years later. What total interest did he pay?
Show answer Hide answer
Answer: A. Rs.635.50
Calculating the compound interest for the first two years gives the total accumulated debt before payment. Subtracting the partial payment of two thousand two hundred ten rupees leaves the remaining principal balance. Co...