Let α and let α,β be the roots of the equation x² + 60^(1/4)x + a = 0. If α ⁴ + β ⁴ = - 30, then the product of all possible values of a is _ _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2023 Mathematics question

JEE Main 2023 · 25 Jan, Evening shift · Q50

JEE Main 202325 Jan, Evening shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

\alpha \in\mathbb{R}

and let

\alpha,\beta

be the roots of the equation

{x^2} + {60^{{1 \over 4}}}x + a = 0

. If

{\alpha ^4} + {\beta ^4} = - 30

, then the product of all possible values of

a

is ____________.

Your answerType your answer. Integers and decimals are accepted.