| Summary: | We explore the quadratic form of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow><mo>=</mo><mi>R</mi><mo>+</mo><mi>b</mi><msup><mi>R</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> gravitational theory to derive rotating <i>N</i>-dimensions black hole solutions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mi>i</mi></msub><mo>,</mo><mi>i</mi><mo>≥</mo><mn>1</mn></mrow></semantics></math></inline-formula> rotation parameters. Here, <i>R</i> is the Ricci scalar and <i>b</i> is the dimensional parameter. We assumed that the <i>N</i>-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter <i>b</i>, whereas, in the case of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>N</mi><mo>></mo><mn>4</mn></mrow></semantics></math></inline-formula>, it depends on parameter <i>b</i>, owing to the contribution of the correction <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter <i>b</i> to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>b</mi><mo><</mo><mfrac><mn>1</mn><mrow><mn>16</mn><mi mathvariant="normal">Λ</mi></mrow></mfrac></mrow></semantics></math></inline-formula> to obtain a positive entropy.
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