Specify the p-value at which the value of the fraction p²-3p-10 divided by p-3p² is equal to zero.

In order to find those values of the variable p that turn the fraction to zero, consider it. The fraction is known to be zero when the numerator is zero and the denominator is nonzero.

That is, we have to solve the following equations: p ^ 2 – 3p – 10 = 0 and p – 3p² ≠ 0.

Let’s solve the full quadratic equation:

p ^ 2 – 3p – 10 = 0;

We are looking for the discriminant:

D = b ^ 2 – 4ac = (- 3) ^ 2 – 4 * 1 / (- 10) = 9 + 40 = 49.

р1 = (- b – √D) / 2a = (3 – 7) / 2 = – 4/2 = – 2;

p2 = (- b + √D) / 2a = (3 + 7) / 2 = 10/2 = 5.

Let’s find the values of the variable p that turn the denominator to zero.

p – 3p² ≠ 0;

p (1 – 3p) ≠ 0;

p ≠ 0; p ≠ 1/3.

Answer: this fraction is equal to zero when p = – 2 and p = 5.