SOLUTION: I don't quite understand what the question is asking. Could you help me solve this problem? Directions: Logical Reasoning - Consider the equations {{{ ax^2 + bx + c=0}}} and

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: I don't quite understand what the question is asking. Could you help me solve this problem? Directions: Logical Reasoning - Consider the equations {{{ ax^2 + bx + c=0}}} and      Log On


   

Question 581080: I don't quite understand what the question is asking. Could you help me solve this problem?
Directions: Logical Reasoning - Consider the equations +ax%5E2+%2B+bx+%2B+c=0 and use the quadratic formula to justify the statement.
If +b%5E2-4ac+ is positive, then the equation has two solutions.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The quadratic formula is:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
It applies to the general quadratic equation:
+ax%5E2+%2B+bx+%2B+c+=+0
You can see there is a " +- " before the
square root sign. That means there are 2 solutions:
x%5B1%5D+=+%28-b+%2B+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
and
x%5B2%5D+=+%28-b+-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
If the +sqrt%28+b%5E2-4%2Aa%2Ac+%29+ term is zero,
then +x%5B1%5D+=+x%5B2%5D+ and there is 1 solution
but if this term is positive, then +x%5B1%5D+
and +x%5B2%5D+ are different and there will be 2 solutions
Hope this helps