which one has no solution?

Question

Which of the following quadratic equations has no solution?

 

A. 0=-3(x+1)(x-8)

B. 0=3(x+1)(x-8)

C. 0=-3(x+1)²+8

D. 0=3(x+1)²+8

Answer 1

C and D are written in vertex form, which makes their inspection particularly easy. 

 

The vertex form is:  y = a(x-h)² + k.

 

The vertex is located at (h,k).

The sign of a indicates the direction in which the parabola opens:

upwards for a>0, and downwards for a<0.

 

If a parabola has a vertex above the x-axis (y=0) and opens upwards, it will never touch the x-axis; that is, be equal to 0.  Do either C or D match this description?

Answer 2

As an exercise, it is instructive to expand (use FOIL) each of the expressions and to collect terms, before determine whether the expression on the right side could be equal to 0.

 

Then, compare you answer to your answer to this [we substitute]:

  If a>0 and b is any number, which of the following cannot equal 0:

      -3ab        [no, b could equal 0]

       3ab        [no, b could equal 0]

      -3a²+8     [no, 3a² could equal 8]

       3a²+b      [well, they are both positive]