Question

Which describes the solutions of the equation?

Answer 1

Option A:

Since 7 and 11 are both rational, the sum and difference are rational.

Solution:

Given equation:

$p^{2}-14 p-72=0$

$p^{2}-14 p=72$

Add 49 on both sides of the equation.

$p^{2}-14 p+49=72+49$

$p^{2}-7p -7 p+49=121$

$p(p-7) -7( p-7)=121$

Take common factor (p - 7) outside.

$(p-7)( p-7)=11^2$

$(p-7)^2=11^2$

Taking square root on both sides.

p - 7 = ±11

p = ±11 + 7

i.e., p = 11 + 7,   p = -11 + 7

11 and 7 are rational numbers.

So the sum and and difference is also rational.

Option A is the correct answer.

Since 7 and 11 are both rational, the sum and difference are rational.