Question 1209150
<br>
{{{x^2 + sx + 144 - 6x + 3x^2}}} = {{{4x^2+(s-6)x+144}}}<br>
In the simplified polynomial, the leading term is {{{4x^2}}}, so the leading term of the square root is {{{sqrt(4x^2)}}} = {{{2x}}}.<br>
The constant term of the simplified polynomial is 144, so the constant term of the square root is {{{sqrt(144)}}} = {{{12}}}.<br>
So the possible square root polynomials are {{{2x+12}}} and {{{2x-12}}}.<br>
{{{(2x+12)^2 = 4x^2+48x+144}}} so for one solution we have<br>
{{{s-6=48}}} --> {{{s=54}}}<br>
{{{(2x-12)^2 = 4x^2-48x+144}}} so for a second solution we have<br>
{{{s-6=-48}}} --> {{{s=-42}}}<br>
ANSWERS: s=54 and s=-42<br>