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Home » Hence, the total number of lattice points is $\boxed30$. - IX Labs

Hence, the total number of lattice points is $\boxed30$. - IX Labs

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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We need the square of the sum of the roots:
\[ (r_1 + r_2)^2 = 5^2 = 25 \]
Thus, the square of the sum of the roots is:
Question: The functions \( f(x) = x^2 - 3x + k \) and \( g(x) = x^2 -...
For \( f(x) \):
\[ f(3) = 3^2 - 3 \cdot 3 + k = 9 - 9 + k = k \]
For \( g(x) \):
\[ g(3) = 3^2 - 3 \cdot 3 + 2k = 9 - 9 + 2k = 2k \]
Since \( f(3) = g(3) \), we have:
\[ k = 2k \]

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