$6x^4+17x^2+7$ can be rewritten as $(3x^2+a)(2x^2+b)$... or as $(3x^2…

Question

Prompt

6 x^{4} + 17 x^{2} + 7

can be rewritten as

(3 x^{2} + a) (2 x^{2} + b)

... or as

(3 x^{2} + c) (2 x^{2} + d)

where

c, d

are nonintegers. What is the value of

a + c