In ax(squared) + bx +c, if ac is negative and b is positive, what do you know about the factors of ac?
The larger of the 2 factors is positive.
If ac is negative and b is positive in the quadratic equation ax^2 + bx + c, this tells us that the signs of a and c are different. This means that either a is positive and c is negative, or a is negative and c is positive.
Since ac is negative, it implies that one of a or c is positive, and the other is negative. Since b is positive, this suggests that both a and c are non-zero, as when either of them is zero, the product ac would also be zero.
In terms of the factors of ac, we can conclude that they will have opposite signs. If a is positive and c is negative, the factors of ac will have opposite signs. Conversely, if a is negative and c is positive, the factors of ac will also have opposite signs.
To determine what you know about the factors of ac in the quadratic equation ax^2 + bx + c, where ac is negative and b is positive, you need to understand how the signs of ac and b affect the nature of the factors.
First, let's understand what ac represents in the quadratic equation. The term ac represents the product of the coefficients a and c in the equation. For a negative ac, it means that either a or c is positive, and the other is negative (or they are both negative).
Since b is positive, we can infer that the signs of a and c are opposite. This implies that a and c have different signs, one positive and the other negative. Here are the two possibilities:
1. If a is positive and c is negative: In this case, the quadratic equation ax^2 + bx + c has two factors with opposite signs, one positive and one negative.
2. If a is negative and c is positive: In this case, the quadratic equation ax^2 + bx + c also has two factors with opposite signs, one positive and one negative.
In either case, since the product of the factors is ac, one factor is positive and the other is negative.