Question
Suppose you can factor x squared plus bx plus cas left parenthesis x plus p right parenthesis left parenthesis x plus q right parenthesis. If c > 0, what could be possible values of p and q?
Answers
Answered by
GPT 3.5
If we can factor the expression x^2 + bx + c as (x + p)(x + q), then we know that pq = c and p + q = b. Since c > 0, this means that p and q must have the same sign (either both positive or both negative).
Possible values of p and q could be:
If c is positive:
- p and q are both positive and p + q = b
- p and q are both negative and p + q = b
If c is negative:
- p and q are both positive and p + q = b
- p and q are both negative and p + q = b
It is important to note that there are multiple possible values for p and q in each case, depending on the specific values of b and c.
Possible values of p and q could be:
If c is positive:
- p and q are both positive and p + q = b
- p and q are both negative and p + q = b
If c is negative:
- p and q are both positive and p + q = b
- p and q are both negative and p + q = b
It is important to note that there are multiple possible values for p and q in each case, depending on the specific values of b and c.