The mean proportional between (13 + 8\(\sqrt{5}\)) and (10 − 2\(\sqrt{5}\)) is:
10\(\sqrt{2}\)
5\(\sqrt{2}\)
\(\sqrt{54+50\sqrt{5}}\)
\(\sqrt{50+54\sqrt{5}}\)
If both roots of the quadratic equation, \( x^{2} + 3x + 2 = 0 \), are also roots of another quadratic equation, \( ax^{2} + bx + c = 0 \), then which of the following must be true?
a + 3b + 2c = 0
a = b = c
\( \frac{a}{1} \) = \( \frac{b}{2} \) = \( \frac{c}{3} \)
\( ax^{2} + bx + c \) must be a multiple of \( x^{2} + 3x + 2 \)