Question

In the equation, p and t are constants. What is the value of p? 4x^2-9=(px+t)(px-t)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the value of p, we will expand the right side of the equation:

(px + t)(px - t) = p^2x^2 - pt^2 - pt^2 + t^2
= p^2x^2 - 2pt^2 + t^2

Comparing this with the given equation 4x^2 - 9, we see that p^2 = 4 and 2pt^2 = 9.

From the first equation, we find that p = 2 or -2.

From the second equation, when p = 2, we get 2t^2 = 9 => t^2 = 9/2 => t = ±3/√2.

Therefore, the value of p can be 2 or -2 depending on the given values of t.