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JEE Main 20246 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Quadratic Equation

JEE Main 2024 · 6 April · Morning Shift · Mathematics · Quadratic Equation

Let x_1, x_2, x_3, x_4 be the solution of the equation 4 x^4+8...

Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be the solution of the equation 4x4+8x3−17x2−12x+9=0and(4+x12)(4+x22)(4+x32)(4+x42)=12516m4 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 mm is

Correct answer

0

Step-by-step solution

4x4+8x3−17x2−12x+9=4(x−x1)(x−x2)(x−x3)(x−x4)\begin{aligned} & 4 x^4+8 x^3-17 x^2-12 x+9 \\ & =4\left(x-x_1\right)\left(x-x_2\right)\left(x-x_3\right)\left(x-x_4\right) \end{aligned}
Put x=2i&−2ix=2 i \&-2 i64−64i+68−24i+9=(2i−x1)(2i−x2)(2i−x3)(2i−x4)=141−88i....(1)64+64i+68+24i+9=4(−2i−x1)(−2i−x2)(−2i−x3)(−2i−x4)=141+88i....(2)\begin{aligned} & 64-64 i+68-24 i+9=\left(2 i-x_1\right)\left(2 i-x_2\right)\left(2 i-x_3\right) \\ & \left(2 i-x_4\right) \\ & =141-88 i ....(1)\\ & 64+64 i+68+24 i+9=4\left(-2 i-x_1\right)\left(-2 i-x_2\right)(-2 i \\ & \left.-x_3\right)\left(-2 i-x_4\right) \\ & =141+88 i....(2) \end{aligned}12516 m=1412+88216 m=221\begin{aligned} & \frac{125}{16} \mathrm{~m}=\frac{141^2+88^2}{16} \\ & \mathrm{~m}=221 \end{aligned}$$
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