Question

How do the signs of b and c in standard form, x^2 + bx + c, affect the signs of p and q in factored form, (x + p)(x + q)?

Answer 1

• c > 0, sign(p) = sign(q) = sign(b)
• c < 0, sign(p) ≠ sign(q)

Explanation:

You want to know the relationship between the signs of 'b' and 'c' in the standard form quadratic x² +bx +c to the signs of 'p' and 'q' in the factored form (x +p)(x +q).

Expansion

Expanding the factored form, we get ...

(x +p)(x +q) = x² +(p+q)x +pq

Comparing this to the standard form, we se that ...

• b = p+q
• c = pq

Signs are related accordingly:

• c > 0 means signs of p and q are the same, and match the sign of b
• c < 0 means signs of p and q are opposites. The sign of the one with the larger magnitude will match the sign of b.