solve the quadratic equation, 2x^2 + 4x = - 12. Which of the following expresses its solutions in the form a ± bi?
-1 ± i√7
-2 ± 2i√5
-1 ± i√5
1 ± i√5
To solve the quadratic equation 2x^2 + 4x = -12, we first rewrite it in the standard form: 2x^2 + 4x + 12 = 0.
Next, we can use the quadratic formula to find the solutions:
x = (-b ± √(b^2 - 4ac)) / (2a),
where a, b, and c are the coefficients from the quadratic equation.
In this case, a = 2, b = 4, and c = 12.
x = (-4 ± √(4^2 - 4(2)(12))) / (2(2))
= (-4 ± √(16 - 96)) / 4
= (-4 ± √(-80)) / 4.
Since √(-1) = i, we can simplify further:
x = (-4 ± √(16) * √(-5)) / 4
= (-4 ± 4i√5) / 4
= -1 ± i√5.
Therefore, the correct answer is -1 ± i√5.