what is the complex number system of Y=2x^2-x+5 and y=3x+5

Question

I neeed to find out what are the complex numbers

 

Answer 1

Giiven equations y = 2x^2-x+5 and y = 3x+5

3x+5 = 2x^2-x+5

Bring all terms to one side.

2x^2-x-3x+5-5 = 0

2x^2-4x = 0

Common out 2x.

2x(x-2) = 0

2x = 0 and x-2 = 0

x = 0 and x = 2

To find the y values substituting each value of x in to linear equation y = 3x+5

For x = 0 ⇒ y = 0+5

y = 5

For x = 2 ⇒ y = 3*2+5

y = 11

There are real solutions (0,5) and (2,11).