Question

The roots of the equation -6x2 + 24x + 12 = 0 are

a) Real, rational, and equal.
b) Imaginary.
c) Real, irrational, and unequal.
d) Real, rational, and unequal.

Answer 1

The roots of the equation -6x ² + 24x + 12 = 0 are real, irrational, and unequal.

Step-by-step explanation:

The roots of the equation -6x ² + 24x + 12 = 0 can be found using the quadratic formula:

x = (-b ± √(b ² - 4ac)) / (2a)

For this equation, a = -6, b = 24, and c = 12.

Plugging in these values into the formula:

x = (-24 ± √(24 ² - 4(-6)(12))) / (2(-6))

Simplifying:

x = (-24 ± √(576 + 288)) / (-12)

x = (-24 ± √864) / (-12)

x = (-24 ± √(16 * 54)) / (-12)

x = (-24 ± 4√54) / (-12)

x = (-24 ± 2√54) / (-6)

x = (-24 ± 2√(9 * 6)) / (-6)

x = (-24 ± 2√9√6) / (-6)

x = (-24 ± 2 * 3√6) / (-6)

x = (-24 ± 6√6) / (-6)

x = -4 ± √6

Therefore, the roots of the equation are real, irrational, and unequal, which corresponds to option c).