In ax(squared) + bx +c, if ac is negative and b is positive, what do you know about the factors of ac?
ac method of factoring is to find out the factors of the product of x^2 coefficient, a and constant term c and such that their sum is equal to b, if ac is positive and if ac is negative their difference is equal to b
To determine what you know about the factors of ac in the quadratic equation ax² + bx + c, where ac is negative and b is positive, you first need to understand the relationship between ac and the discriminant of the quadratic equation.
The discriminant (Δ) is given by the formula Δ = b² - 4ac. This value determines the nature of the roots of the quadratic equation. It can be positive, zero, or negative.
Now, if ac is negative, it means that a and c have opposite signs. Since b is positive, we know that b² is also positive.
In order for the discriminant Δ to be positive, b² - 4ac must be greater than zero. This inequality can be simplified as:
b² > 4ac
Since b² is positive, in order for the inequality to hold, 4ac must be negative. This means that either a or c (or both) must be negative.
Therefore, we can conclude that if ac is negative and b is positive, at least one of the factors of ac must be negative.
To summarize, if ac is negative and b is positive, the factors of ac have opposite signs, and at least one of them is negative.