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special right triangles (radical answers)

x =

Step-by-step explanation:

Since the given triangle is equilateral the all 3 sides would be:

or . Now we know that the base of the right triangle is and the hypotenuse is . Therefore we can say;

A² + B² = C²

()² + x² = ()²

6 + x² = 12

x² = 12 - 6

x² = 6

x =

Therefore; x = is the length of x, in simplest radical form.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.

step-by-step explanation: