Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
Most Important Selected Qs for JEE AdvancedMathematicsTrigonometry

If sum of the roots of the equation 2 (x+ 4 ) ( ^2 x-(1+ 3 ) x+2+ 3 )= 9+18 x x in [0,2 ] is p q where p, q N , then find the least value of |p-q| .

Correct answer

25

Step-by-step solution

aligned & (25)( x+ x) ( ^2 x-(1+ 3 ) x+3+ 3 )=3| x+ x| & Case-1: x+ x 0 & ( x+ x) ( ^2 x-(1+ 3 ) x+ 3 )=0 & x=-1,1, 3 & x= 3 4 , 4 , 3 , 7 4 & Case-2: x+ x < 0 & ( x+ x) ( ^2 x-(1+ 3 ) x+6+ 3 ) _ no solution =0 & aligned aligned & x=-1 x= 3 4 , 7 4 & Required sum = 37 12 aligned

Practice Trigonometry on Quantrex Academy →

More from Trigonometry

The number of real root(s) of the equation x^2 x=1 lie(s) between 0 and 2 is/areIf |x^2- 4 + x-2 |= |x^2-2 |+| x|+ 4 thenIf 3 x+ (2 x- 7 6 )=-2 , then x is equal to ( where m I)What is the minimum value of ^4 ^2 + ^4 ^2 for , B k 2 , k Z ?If x+ y x x R then y+ is equal toIf A, B are the roots of the quadratic equation a b x^2-c^2 x+a b=0 where a, b, c are sides of the A B C then ^2 A+ ^2 B+ ^2 C isIf and - are the roots of the equation a x^2-b x-c=0 , where a, b, c are the sides of a triangle A B C , then B is equal toIf 2 ^2 ( 2 ^2 x )=1- ( 2 x), x (2 n+1) 2 , n I , then Full Trigonometry list All Most Important Selected Qs for JEE Advanced PYQs