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However, some applications need to compute real eigenvalues only. We propose a Lanczos\u2010based method for computing all real eigenvalues contained in a given interval of large\u2010scale symmetric QEPs. The method uses matrix inertias of the quadratic polynomial evaluated at different shift values. In this way, for hyperbolic problems, it is possible to make sure that all eigenvalues in the interval have been computed. We also discuss the general nonhyperbolic case. Our implementation is memory\u2010efficient by representing the computed pseudo\u2010Lanczos basis in a compact tensor product representation. 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