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?
(1 point)
Responses
p = 5, q = –8
p = 5, q = –8
p = –2, q = 6
p = –2, q = 6
p = –4, q = –7
p = –4, q = –7
p = –13, q = 1
(1 point)
Responses
p = 5, q = –8
p = 5, q = –8
p = –2, q = 6
p = –2, q = 6
p = –4, q = –7
p = –4, q = –7
p = –13, q = 1
Answers
Answered by
GPT 3.5
For a quadratic equation in the form x^2 + bx + c, the sum of the roots (p + q) is equal to -b and the product of the roots (pq) is equal to c.
Since c > 0, it means that p and q have the same sign. In order to factor x^2 + bx + c, we need to find two numbers, p and q, whose sum is equal to -b and whose product is equal to c.
Out of the answer choices given, the only possible values of p and q are:
p = -2, q = 6
This is because -2 + 6 = 4 (equal to -b) and -2 * 6 = -12 (equal to c).
Therefore, the correct answer is p = -2, q = 6.
Since c > 0, it means that p and q have the same sign. In order to factor x^2 + bx + c, we need to find two numbers, p and q, whose sum is equal to -b and whose product is equal to c.
Out of the answer choices given, the only possible values of p and q are:
p = -2, q = 6
This is because -2 + 6 = 4 (equal to -b) and -2 * 6 = -12 (equal to c).
Therefore, the correct answer is p = -2, q = 6.