\[ (3k)(2k) = 6k^2 = c \]

February 22, 2026

$(3k)(2k) = 6k^2 = c$

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Let the roots be \( 3k \) and \( 2k \). By Vieta's formulas, the sum of the roots is:
\[ 3k + 2k = 5k = -b \]
\[ b = -5k \]
We need values for \( b \) and \( c \) in terms of \( k \). To find \( k \), note that the roots are real numbers, and any \( k \) will satisfy the conditions provided \( b \) and \( c \) are expressed as above. However, for simplicity, we can express them in terms of \( b \) and \( c \):
From \( b = -5k \), we have \( k = -\frac{b}{5} \).
Substitute into the expression for \( c \):

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