Suppose you can factor x^2 +bx +c as (x+p)(x+q) . if c< 0, what could be the possible values of p and q? a: p= -3, q= 7 b: p= 11, q= 4 c: p= -2, q= -5 d: p= 1, q= 10

Ans: Option A

Explanation:
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Given expression:  --- (A)
Factors: (x+p)(x+q)

Condition: c<0

Now let us expand (x+p)(x+q):
=>  --- (B)

By comparing (B) with (A), we can say that:

pq = c --- (C)

Now, as the condition says, c<0, it means either p or q is negative. Both cannot be positive or both cannot be negative.

1) If p>0, q>0, it means c>0 since (+p)(+q) = (+c)(according to equation (C)). Condition is not met.
Hence, option B and D are wrong.

2) If p<0, q<0 it means c>=0 since (-p)(-q) = (+c)(according to equation (C)). Condition is not met.
Hence option C is out as well.

We are left with Option A:
p<0, q>0 it means c<0 since (-p)(+q) = (-c)(according to equation (C)). Condition is MET!
Hence,
Ans: Option A: p= -3, q= 7

What you should know is that the value of c will be given by the following product:
 c = p * q
 So that c <0
 We have that the possible values are:
 p = -3
 q = 7
 Thus, the value of c is:
 c = p * q
 c = (- 3) * (7)
 c = -21 <0
 
 the possible values of p and q could be
 A: p = -3, q = 7