Let x₁, x₂, x₃, x₄ be the solution of the equation 4 x⁴+8 x³-17 x²-12 x+9=0 and (4+x₁²)(4+x₂²)(4+x₃²)(4+x₄²)=125/16 m. Then the value of m is _ _ _ _ _.

Complex Numbers and Quadratic Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 6 Apr, Morning shift · Q45

JEE Main 20246 Apr, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

Let

x_1, x_2, x_3, x_4

be the solution of the equation

4 x^4+8 x^3-17 x^2-12 x+9=0

and

\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m

. Then the value of

m

is _________.

Your answerType your answer. Integers and decimals are accepted.