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No real roots, quadratic in disguise

Source: LIMIT 2020 Cat 2 Obj P3

May 25, 2020
limitalgebra

Problem Statement

Given that the equation (m2−12)x4−8x2−4=0(m^2-12)x^4-8x^2-4=0 has no real roots, then the largest value of mm is pqp\sqrt{q}, where pp and qq are natural numbers, qq is square-free. Determine p+qp+q.
(A)44 (B)55 (C)33 (D)66
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