Question

If p and q are the solutions to x + 13x = 48, then what is the value of (p − q) ? A. 289 B. 361 C. 441 D. 400

Answer 1

Answer:

If p and q are the solutions to x + 13x = 48, then what is the value of (p − q) ? A. 289 B. 361 C. 441 D. 400

Answer 2

Answer:

Step-by-step explanation:

According to the question,

$x^2+13x= 48 \\means \\x^2+13x-48$

Factoring  $x^2+13x-48$

The first term is,  $x^2$  its coefficient is  1.

The middle term is,  $13x$  its coefficient is  13.

The last term, "the constant", is  -48.

the polynomial splitting the middle term using the two factors found above,  -16  and  3

                    $x^2 + 16x - 3x - 48$

Add up the first 2 terms, pulling out like factors :

          $x . (x+16)$

             Add up the last 2 terms, pulling out common factors :

                    $3 . (x+16)$

Add up the four terms:

                       $(x-3) . (x+16)$

            Which is the desired factorization.

$(x - 3) . (x +16) = 0$

the solution is -16 and 3.

$p = -16\\\\q = 3\\\\then, \\\\p-q = -16 -3 = -19$.