Solve equations (i). a2 – 7a + 12 = 0 and (ii). b2 – 3b + 2 = 0 to determine a and b?
Show answer Hide answer
Answer: D. if a > b
Explanation
Equation one factors into a minus three times a minus four equals zero, yielding roots three and four. Equation two factors into b minus one times b minus two equals zero, yielding roots one and two. Comparing all possible root combinations shows that every value of a is strictly greater than every value of b. Quadratic equations can be solved by factoring polynomials into binomial products to find root values. Comparing two sets of roots determines inequality relationships between variables across all possible solutions. Inequality comparisons evaluate whether one variable is consistently greater than or equal to another.
Comparative algebraic analysis is used in optimization problems to determine dominance relationships between functions. Automated reasoning systems evaluate inequalities to establish boundaries in constraint satisfaction programs. Mathematical aptitude assessments test root comparison techniques to evaluate quadratic equation proficiency. Option A is incorrect because variable a is consistently greater than variable b, not smaller. Option B is false because there is no overlap where variable a is less than or equal to b. Option C is incorrect because a definitive inequality relationship can be established between the roots.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. 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...
Q2. 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...
Q3. Solve equations I. x2 + 9x + 20 = 0 and II. y2 + 5y + 6 = 0 to determine x and y?
Show answer Hide answer
Answer: A. If x < y
Solving equation one yields roots of negative four and negative five via standard quadratic factoring. Solving equation two yields roots of negative two and negative three through binomial factorization. Comparing all re...
Q4. 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...
Q5. 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...
Q6. Ramees purchases goods valued at Rs. 6650 with a 6% rebate, then pays a 10% sales tax on the discounted amount. Find his total payment.
Show answer Hide answer
Answer: A. Rs. 6876.10
Applying a six percent rebate to the base price of sixty six fifty reduces the cost. Calculating ten percent sales tax on this discounted price adds the mandatory government tax amount. Summing the discounted price and t...