A product of two expressions involving can lead to a quadratic equation, an equation with an term. Write the second number in terms of , then multiply to match the given product. A Desmos regression can find quickly; restrict it to positive values when the question requires one. Don't mistake the smaller factor for the number named .
Hints
- Hint 1
In “ less than ,” start with and subtract . The order matters: what expression represents the smaller number?
- Hint 2
A product means multiplication. Once you've written both numbers using , multiply their expressions and set the result equal to .
- Hint 3
Two negative numbers can also have a positive product. When you solve in Desmos, how can you restrict to match the question's requirement that be positive?
Step-by-step
Translate and solve with Desmos
Step 1Write the second number
Start with and subtract , so the other number is . “ less than ” means , not . Keep that subtraction order when you write the product.
- Step 2
Write the product equation
A product means multiply. The numbers are and , and their product is , so
Don't add the numbers; the word “product” calls for multiplication.
- Step 3
Find the positive value
Type in Desmos. The tells Desmos what to solve for, asks it to make the sides equal, and the braces keep only positive values. That restriction matters because two negative numbers can also multiply to . Desmos shows under PARAMETERS, so the positive number is . Choice C.