Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202520 Apr 2025Evening ShiftMathematicsProperties of TrianglesActual

In a triangle ABC , the sides a, ~b , c are such that they are the roots of the equation x^3-11 x^2+38 x-40=0 Then A a + B b + C c =

Options

  1. A3 4
  2. B1
  3. C9 16
  4. D1 16

Correct answer

C. 9 16

Step-by-step solution

The sides of the triangle are the roots of the equation x^3 - 11x^2 + 38x - 40 = 0 . Testing integer divisors of 40 reveals that x = 2 is a root. Dividing the cubic polynomial by (x - 2) yields x^2 - 9x + 20 , which factors as (x - 4)(x - 5) . The sides are therefore 2 , 4 , and 5 in some order. Using the Law of Cosines, A = b^2 + c^2 - a^2 2bc , with similar expressions for B and C . Substituting into A a + B b + C c gives b^2 + c^2 - a^2 2abc + a^2 + c^2 - b^2 2abc + a^2 + b^2 - c^2 2abc . The sum simplifies to a

Practice Properties of Triangles on Quantrex Academy →

More from Properties of Triangles

In A B C , if A, B, C are in arithmetic progression then a ^2- ac + c ^2 ( ~A - C 2 )= 2025If in A B C, B=45^ , a=2( 3 +1) and area of A B C is 6+2 3 sq.units, then the side b = 2025In triangle A B C , if C=120^ , c= 19 and b=3 , then a= 2025In a A B C, 2 A+C=300^ . If the circumradius of the A B C is eight times its inradius then C 2 = 2025In A B C , if a=5, b=4 and (A-B)= 31 32 , then c= 2025In a triangle ABC, if A =30^ and b ( 3 +1)^2+2( 2 -1) = c ( 3 +1)^2-2( 2 -1) , then B= 2025In ABC if the line joining the circumcentre and the incentre is parallel to BC, then B + C = 2025In a triangle ABC, if r ₁: r ₂=3: 4 and r ₂: r ₃=2: 3 , then a : b : c = 2025 Full Properties of Triangles list All MHT CET PYQs