Final answer:
Yes, Kelsey can use the quadratic formula to solve the equation x⁴ - 5x² - 5 = 0. The quadratic formula is given by: x = (-b ± √(b² - 4ac)) / (2a). For the equation x⁴ - 5x² - 5 = 0, the solutions for x are x = √(20) / 2 and x = -√(20) / 2.
Step-by-step explanation:
Yes, Kelsey can use the quadratic formula to solve the equation x⁴ - 5x² - 5 = 0. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
For the equation x⁴ - 5x² - 5 = 0, we can see that a = 1, b = 0, and c = -5. Substituting these values into the quadratic formula, we get:
x = (-0 ± √(0² - 4(1)(-5))) / (2(1))
Simplifying further:
x = ± √(20) / 2
Therefore, the two solutions for x are x = √(20) / 2 and x = -√(20) / 2.