Mathematics · Quadratic EquationsJEE Main 2024 — 6 April, Shift 1 — Question 24Let x1,x2,x3,x4x_{1}, x_{2}, x_{3}, x_{4}x1,x2,x3,x4 be the solution of the equation 4x4+8x3−17x2−12x+9=04 x^{4}+8 x^{3}-17 x^{2}-12 x+9=04x4+8x3−17x2−12x+9=0 and (4+x12)(4+x22)(4+x32)(4+x42)=12516m\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(4+x12)(4+x22)(4+x32)(4+x42)=16125m . Then the value of mmm is \qquadAnswer: 221Numerical answer — enter this value.Step-by-step solution4x4+8x3−17x2−12x+94 \mathrm{x}^{4}+8 \mathrm{x}^{3}-17 \mathrm{x}^{2}-12 \mathrm{x}+94x4+8x3−17x2−12x+9 =4(x−x1)(x−x2)(x−x3)(x−x4)=4\left(\mathrm{x}-\mathrm{x}_{1}\right)\left(\mathrm{x}-\mathrm{x}_{2}\right)\left(\mathrm{x}-\mathrm{x}_{3}\right)\left(\mathrm{x}-\mathrm{x}_{4}\right)=4(x−x1)(x−x2)(x−x3)(x−x4) Put x=2i&−2ix=2 \mathrm{i} \&-2\mathrm{i}x=2i&−2i 64−64i+68−24i+9=(2i−x1)(2i−x2)(2i−x3)64-64 \mathrm{i}+68-24 \mathrm{i}+9=\left(2 \mathrm{i}-\mathrm{x}_{1}\right)\left(2 \mathrm{i}-\mathrm{x}_{2}\right)\left(2 \mathrm{i}-\mathrm{x}_{3}\right)64−64i+68−24i+9=(2i−x1)(2i−x2)(2i−x3) (2i−x4)\left(2 \mathrm{i}-\mathrm{x}_{4}\right)(2i−x4) =141−88i=141-88 \mathrm{i}=141−88i 64+64i+68+24i+9=4(−2i−x1)(−2i−x2)(−2i−x3)64+64 \mathrm{i}+68+24 \mathrm{i}+9=4\left(-2 \mathrm{i}-\mathrm{x}_{1}\right)\left(-2 \mathrm{i}-\mathrm{x}_{2}\right)(-2\mathrm{i} \left.-\mathrm{x}_{3}\right)64+64i+68+24i+9=4(−2i−x1)(−2i−x2)(−2i−x3) (−2i−x4)=141+88i\left(-2 \mathrm{i}-\mathrm{x}_{4}\right) =141+88 i(−2i−x4)=141+88i 12516 m=1412+88216\frac{125}{16} \mathrm{~m}=\frac{141^{2}+88^{2}}{16}16125 m=161412+882 m=221m=221m=221Answer key and solution verified before publishing.Practise Quadratic EquationsStart with this question, then two more from the same chapter — with a tutor that explains every step. Free.Solve a similar one free→ExamJEE Main 2024Paper6 April, Shift 1SubjectMathematicsChapterQuadratic EquationsTopicTheory of Equations of Degree other than 2← Question 23Let r k=fracint 0^1 (1-x^7 )^k d xint 0^1 (1-x^7 )^k+1 d x, k in N . Then the value of sum k=1^10 frac17 ( r k-1 ) is equal toQuestion 25 →Let L 1, L 2 be the lines passing through the point P(0,1) and touching the parabola 9 x^2+12 x+18 y-14=0 . Let Q and R be the points on…More Quadratic Equations questions from this paperLet, alpha, beta be the distinct roots of the equation x^2- (t^2-5 t+6 ) x+1=0, t in R and a n=alpha^n+beta^n . Then the minimum value of…