Determine the number and type of complex solutions and possible real solutions for each of the following equations.

Question

1) 2x² + 5x + 3 = 0

 

2)  4x³ – 12x + 9 = 0

3)  2x⁴ + x² – x + 6 = 0

Answer 1

1) Since this is degree 2, it will have 2 zeros. When I graph this, I can see 2 x intercepts. Therefore there are 2 real zeros. You could also look at the discriminant. The value of b²-4ac (5²-4(2)(3) = 1) is positive, so there are 2 real zeros.

2) Since this is degree 3, it will have 3 zeros. When I graph this, I can see 2 x intercepts. Therefore there is 1 real zeros. Since the total must be 3, this tells me there are 2 complex zeros.

3) Since this is degree 4, it will have 4 zeros. When I graph this, I can see there are no x intercepts. Therefore there are no real zeros. Since the total must be 4, this tells me there are 4 complex zeros.