A quadratic equation is shown below 9x^2-36x+36=0

A Determine the radicand discriminat... the number under the radical sign tell how many solutions this equation has and indicate how you know based on the radicand show your work

B solve 2x^2-9x+7 for using x an appropriate method show the steps of your work

9514 1404 393

  A.  d = 0 -- one (1) solution

  B.  x = {1, 3.5}

Step-by-step explanation:

A. The discriminant for ax²+bx+c = 0 is ...

  d = b² -4ac

For the given equation, this is ...

  d = (-36)² -4(9)(36) = 0

The discriminant is zero (0).

The discriminant divided by the leading coefficient (a=2) will give the difference between the two roots of the equation. When the difference is zero, as here, both roots are the same. Effectively, there is one (1) solution to the equation.

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B. The equation can be factored as ...

  2x² -9x +7 = (2x -7)(x -1) = 0

The solutions are the values of x that make the factors be zero:

  2x -7 = 0  ⇒  x = 7/2

  x -1 = 0  ⇒  x = 1

  The solutions are x = 7/2  or  x = 1.