Question

What are all real values of a such that the sum of the squares of the roots of
x^2 - 8ax +14a^2 = 0
is 25?

Answer 1

\[a=\pm \frac{5}{6} \]Solve the given equation for a. Square each root and sum the results and simplify.\[36 a^2=25\]Solve the above for a.

To check the results, replace a in the original equation and solve for x.
Sum the square of each root. The sum should be 25.