# Determine if the following equations are real or complex.

Determine if the following equations are real or complex; explain the answer in detail.

Determine whether the following equations real or complex solutions; justify your answer. Note: It is not necessary to find the solutions; just determine if they are real or complex and explain why.

a) 5x2 + 8x + 7 = 0

b) (7)1/2y2 - 6y - 13(7)1/2 = 0

c) 2x2 + x - 1 = 0

d) 4/3x2 - 2x + 3/4 = 0

e) 2x2 + 5x + 5 = 0

f) p2 - 4p + 4 = 0

g) m2 + m + 1 = 0

h) 3z2 + z - 1 = 0

**This is worth alot of points and I am not sure I am doing it correctly I have attached what I have sofar. Thanks in advance for your help and imput.

a) 5x2 + 8x + 7 = 0

8*8 - 4*4*7 = -48 Multiply 8*8 and 4*4

64 -16 * 7 = -48 Multiply -16 * 7

64 - 112 = -48 Subtract

-48 = -48 D = 0

b) (7)1/2y2 - 6y - 13(7)1/2 = 0

6*6 - 4*7.5*13*7.5 = -2889 D < 0

This is complex because D < 0, Roots are not real.

c) 2x2 + x - 1 = 0

1*1 - 4*2*-1 = 9 D = 9

solution is real, because D = 9, Roots are real and equal.

d) 4/3x2 - 2x + 3/4 = 0

-2*-2 - 4*4/3*3/4 = 0

solution is real, because D = 0, Roots are real and equal.

e) 2x2 + 5x + 5 = 0

5*5 - 4*2*5 = -15

this is complex because D < 0, Roots are not real.

f) p2 - 4p + 4 = 0

-4*-4 - 4*1*4 = 0

solution is real, because D = 0, Roots are real and equal.

g) m2 + m + 1 = 0

1*1 - 4*1*1 = -3

This is complex because D < 0, Roots are not real.

h) 3z2 + z - 1 = 0

1*1 - 4*3*-1 = 13

solution is real, because D > 0, but may not be a perfect square

#### Solution Summary

Real and complex roots are determined.