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.