SOLUTION: totally lost quadratic equation ax^2+bx+c=0 solution 8, only solution The equation is ____

SOLUTION: totally lost quadratic equation ax^2+bx+c=0 solution 8, only solution The equation is _____=0

Question 131760: totally lost
quadratic equation
ax^2+bx+c=0
solution 8, only solution
The equation is _____=0

Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Write the quadratic equations () given the solution is x = 8.
Now, quadradic equation have two solutions, so when you say that x = 8 is the only solution, this means the equation has a "double solution" of x = 8 and x = 8.
So, we work backwards from the solutions to the equation as follows:
Start with the solutions:
and This means that the parabola generated by the equation touches the x-axis at the point x = 8,
In solving the equation, there had to be two factors that were equal to zero and these factors are:
and so if we now multiply these factors together, we will arrive at the original equation.
This is the equation.
Check:
We know that if the discriminant () of a quadratic equation is equal to zero, then the equation has a double root.
In this case, the equation we just generated shows us that a = 1, b = 16, and c = 64. Let's see if the discriminant does equal zero.
=
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