SOLUTION: algebra of linear and quadratic expressions. find the values of k for which the quadratic 2x^2+kx+9=0 has one real solution, and another with no real solutions.

Question 155037: algebra of linear and quadratic expressions.
find the values of k for which the quadratic 2x^2+kx+9=0 has one real solution, and another with no real solutions.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the discriminant formula

Plug in , and

Multiply 4 and 2 to get 8

Multiply 8 and 9 to get 72

So we'll use the equation to solve the following:

1) "find the values of k for which the quadratic has one real solution"

If a quadratic has one real solution, then the discriminant is equal to zero. So this means that

Start with the previous equation

Plug in

Add 72 to both sides

Take the square root of both sides

or Break up the "plus/minus"

or Simplify the square root

So if or , then the discriminant is equal to zero. This means that the equation or only has one real solution.

2) "find the values of k for which the quadratic no real solutions"

If a quadratic has no real solutions, this means that the discriminant is less than zero. In other words,

Go back to the previous equation

Since , this means that the right side is less than zero

Add 72 to both sides

Take the square root of both sides

or Break up the "plus/minus"

or Simplify the square root

Recombine the two inequalities to form one compound inequality

So if "k" is in between and , then the discriminant is less than zero. This means that if "k" is in between and , then the quadratic will have no solutions

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