Consider a quadratic equation of the form x? + bx + c = 0, where b and c are rational numbers. Fill in the blanks in the following proof that if one solution is rational, then the other solution is also rational. Proof: Suppose x2 + bx + c = 0 is any quadratic equation where b and c are rational numbers, and suppose one solution r is rational. Call the other solution s. Then x? + bx + c= (x - r)(x - s). Multiply out (x - r)(x - s) and set it equal to x + bx + c to obtain x² + bx + c = x? + ( Equate coefficients and solve for s in terms of b and c to obtain s = Since ---Select- v are --Select-- V and since -Select- v are rational, we conclude that ---Select-- v is rational, and so sis rational.
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Help
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
