Question

Without solving, determine the character of the solutions of the equation in the complex number system.4x2 + 2x= -3Choose the correct answer below.O A. Two unequal real-number solutionsO B. Two complex conjugate solutionsO C.One repeated real-number solution

Answer 1

We can use the discriminant to determine the number and type of solutions.

4x2 + 2x= -3

Rewriting so the solution is equal to zero

4x2 + 2x+3 =0

Using the form

ax^2 +bx +c =0

We can use the discriminant

b^2 -4ac where a=4 b=2 and c = 3

2^2 -4(4)(3)

4 - 48

-44

Since this is <0 there are no real solutions ( there are 2 complex solutions)

if it is >0 there are 2 real solutions

=0 there is one real solution