Question

The arithmetic mean of the roots of the equation 3x ² + 12x + k = o is equal to...?

a) 0 b) 1 c)2 d)3

Answer 1

\[(-b \pm \sqrt{b ^{2}-4ac})/2a\]
this is how you solve quadratic equations hope this is clear.

now b=12 here and the b^2-4ac=12^2-12k
lets call this D, so D=12^2-12k

than the two solutions will be like \[(-12\pm \sqrt{D})/6\]

when we take the arithmetic mean of them, that is just summing the 2 numbers and dividing by two. if we sum -sqrt D and + sqrt D they will cancel

so the solution will (12/6 +12/6) /2=2