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4x^2-9=(px+t)(px-t) In the equation ab...

`4x^2-9=(px+t)(px-t)`
In the equation above, p and t are constants. Which of the following could be the value of p ?

A

2

B

3

C

4

D

9

Text Solution

Verified by Experts

The correct Answer is:
A
The right side of the equation can be multiplied using the distributive property:` (px + t)(px − t) = p^2x^2 − ptx + ptx − t^2`. Combining like terms gives `p^2x^2 − t^2`. Substituting this expression for the right side of the equation gives `4x^2 − 9 = p^2x^2 − t^2`, where p and t are constants. This equation is true for all values of x only when 4 = `p^2` and 9 = `t^2`. If 4 = `p^2`, then p = 2 or p = −2. Therefore, of the given answer choices, only 2 could be the value of p.
Choices B, C, and D are incorrect. For the equation to be true for all values of x, the coefficients of `x^2` on both sides of the equation must be equal, that is, `4 = p^2`. Therefore, the value of p cannot be 3, 4, or 9.
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