Question

What are the roots of the equation x2 + 15x = -57 in simplest a + bi form?

Answer 1

Explanation:

Rewrite x2 + 15x = -57 as x^2 + 15x + 57 = 0, in which the coefficients of this quadratic are {1, 15, 57}.

Then the discriminant is b^2 - 4ac = 225 - 4(1)(57) = -3

Because the discriminant is negative, we know that the two roots will be complex. They are:

-15 ±i√3

x = ---------------

2

Answer 2

9514 1404 393

Answer:

x = -7.5 ± i(√3)/2

Explanation:

We can add (15/2)² to complete the square:

x² +15x +(15/2)² = -57 +(15/2)²

(x +7.5)² = -0.75

x +7.5 = ±i(√3)/2 . . . . take the square root

The roots are ...

`x=\displaystyle\left \{ {{-(15)/(2)+i(√(3))/(2)} \atop {-(15)/(2)-i(√(3))/(2)}} \right.`