State any real numbers that must be excluded from the domain of the rational expression. Enter your answers in increasing order.
6p2/p2−49
any values of p that make the denominator zero must be excluded from the domain.
To find the real numbers that must be excluded from the domain of the rational expression 6p^2/(p^2 - 49), we need to identify any values of p that would make the denominator equal to zero.
Since p^2 - 49 is a quadratic expression, it will be equal to zero when p^2 equals 49. Taking the square root of both sides, we find that p is equal to ±7.
Therefore, the real numbers that must be excluded from the domain of the rational expression are 7 and -7. In increasing order, this can be written as {-7, 7}.
To determine the real numbers that must be excluded from the domain of the rational expression 6p^2 / (p^2 - 49), we need to identify the values of p that would result in a denominator of zero.
In this case, we need to find the values of p such that (p^2 - 49) = 0 since division by zero is undefined.
To solve p^2 - 49 = 0, we can factor the quadratic equation as (p + 7)(p - 7) = 0.
Setting each factor equal to zero gives us two possible solutions: p + 7 = 0 and p - 7 = 0. Solving these equations, we find that p = -7 and p = 7.
Therefore, the values of p that result in a zero denominator are -7 and 7.
To express these real numbers in increasing order, we write: -7, 7.