Julie is solving the equation x2 + 5x + 6 = 0 and notices that the discriminant b2 - 4ac has a value of 1. This tells her that the equation...

To solve the equation x^2+5c+6 = 0.The discriminant is
1.

Solution: A quadratic equation  2nd degree of a single
variable x is like ax^+bx+c = 0, where a, b and c are coefficients.The discriminant of
this equation is b^2-4ac. And the equation has two roots x1 and x2 given by: x1 =
{-b+sqrt(b^2-4ac})}/2a  and x2 =  {-b-sqrt(b^2-4ac})}/2a. Or x1, x2 =
(-b+or-sqrt(discriminant)}/2a.

In our case, x^2+5c+6 = 0,
or1*x^25x+6 = 0, a = 1, b= 5 and c= 5. So the discriminant of x^2+5x+6 = 0 is 5^2-4*1*6
= 25-24 = 1.

Therefore the equation has two
distinct roots  given by:

 x1
= {-5+sqrt(discriminant 1)}/2*1} =  {-5+1}/2 = -2

x2 =
{-5-sqrt(discriminant 1)}/2*1} =  {-5-1}/2 = -3.

So the
roots are of the equation has two roots.

Again be reminded
that discriminant 1 does not mean the equation has single
variable. The discriminant is a different concept. The discriminant gives
a measure of (x1-x2)^2 , the square of the differences of the
roots.

Hope this helps.