Final answer:
The roots of the equation 5x² = -17x - 165x in simplest a+bi form can be found by using the quadratic formula.
Step-by-step explanation:
The roots of the equation 5x² = -17x - 165x in simplest a+bi form can be found by using the quadratic formula. The quadratic formula states that the roots of an equation of the form ax² + bx + c = 0 can be found using the formula:
x = (-b ± √(b² - 4ac))/(2a)
Substituting the values a = 5, b = -17, and c = -165 into the formula, we can calculate the roots:
x = (-(-17) ± √((-17)² - 4(5)(-165)))/(2(5))
x = (17 ± √(289 + 3300))/(10)
x = (17 ± √(3589))/(10)
So, the roots of the equation in simplest a+bi form are:
x = (17 ± √(3589))/(10)