Quadratic equations · solved example
Solve the two equations and choose the correct relation between x and y. I. x^2 - 27x + 180 = 0 II. y^2 - 15y + 56 = 0
- x is greater than yCorrect
- x is less than y
- x is greater than or equal to y
- x is less than or equal to y
- x equals y, or no relation can be established
Solution
For the first, 180 splits as 12 and 15 which add to 27, so x is 12 or 15. For the second, 56 splits as 7 and 8 which add to 15, so y is 7 or 8. The smallest x is 12 and the largest y is 8, so every value of x exceeds every value of y and the relation is strictly greater than, option A. Because the ranges do not touch, the answer is a strict inequality rather than the 'or equal to' form, which is the distinction options A and C exist to test.