Question 233404
For {{{ax^2 + bx +c = 0}}} the roots are:
{{{x = (-b + sqrt(b^2 - 4ac))/(2a)}}}
and
{{{x = (-b - sqrt(b^2 - 4ac))/(2a)}}}
The difference would be:
{{{(-b + sqrt(b^2 - 4ac))/(2a) - (-b - sqrt(b^2 - 4ac))/(2a)}}}
These two fractions have the same denominator so we can go ahead and subtract. The -b's in the numerator cancel and we end up with:
{{{(2sqrt(b^2-4ac))/(2a)}}}
The 2's cancel leaving:
{{{sqrt(b^2-4ac)/a}}}<br>
Using this on your equation we get a difference of:
{{{sqrt((-7)^2 - 4(1)(-9))/((1)) = sqrt(49 + 36) = sqrt(85)}}}
So (e) is the answer.