HELP WHAT IS THIS????

Question

Using the discriminant, determine the number and type of solutions that exist for the quadratic equation x² + 8x + 16 = 0.

Answer 1

For a quadratic equation in the form of ax²+bx+c=0, there are 3 cases for the value of the discriminant that determine the number and type of solutions:

1) If b²-4ac>0, then there are 2 real solutions

2) If b²-4ac<0, then there are 2 imaginary solutions

3) If b²-4ac=0, then there is 1 real solution

In this case, for the quadratic equation x²+8x+16 = 0, our discriminant is 8²-4(1)(16) = 64-64 = 0. This means that there will be only one real solution.

x²+8x+16 = 0

(x+4)² = 0

x = -4

This confirms that there is indeed one real solution because the factor x+4 has a multiplicity of 2.

Hope this helped!