Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20227 Jul 2022Morning ShiftMathematicsDeterminantsActual

If the system of simultaneous linear equations x+y-z=6,4 x+y+z=2 and x+k y+z=-8 has a unique solution x=2 , y= , z= , then the value of k satisfies the following quadratic equation

Options

  1. Ax^2-5 x+6=0
  2. Bx^2+x-6=0
  3. Cx^2-x-6=0
  4. Dx^2+x-2=0

Correct answer

D. x^2+x-2=0

Step-by-step solution

x+y-z=6 aligned & 4 x+y+z=2 & x+k y+z=-8 aligned x=2, y= , z= -3=4 ...(i) y+z=-10 ...(ii) 2 y=-6 y=-3 Put in eq no (i) 3=-7 Now, put values of x, y and z , we get 2+k(-3)+(-7)=-8 -3 k=-3 k=1 check all the options which satisfy this value of k . we get option (d), aligned & x^2+x-2=0 & (1)^2+(1)-2=0 0=0 verified. aligned

Practice Determinants on Quantrex Academy →

More from Determinants

Let A = [a_ ij ] be a square matrix of order 3 3 , where the elements are defined as a_ ij = cases i - 2j & if i = j 0 & if i > j 1 & if i < j cases then the value of |A^t| is 2026Let A be a square matrix of order 3 3 . If |A| = -4 , then the value of | A⁻¹ -2 | is: 2026Given P = bmatrix 2 & & 1 1 & 2 & 2 1 & 3 & 3 bmatrix is the adjoint of a 3 3 matrix A and |A| = 3 , then the value of is: 2026Which of the following is correct? 2026If A and B are invertible square matrices of order n, then which of the following is not correct? 2026The system of equations x + 2y = 3 and 2x + 3y = 3 has 2026A value of lying between 0 and 2 and satisfying | array ccc 1+ ^2 & ^2 & 4 4 ^2 & 1+ ^2 & 4 4 ^2 & ^2 & 1+4 4 array |=0 2025If the inverse of [ array ccc -x & 14 x & 7 x 0 & 1 & 0 x & -4 x & -2 x array ] is [ array ccc 2 & 0 & 7 0 & 1 & 0 1 & -2 & 1 array ] , then | array ccc x & x+1 & x+2 x+1 & x+2 & x 2025 Full Determinants list All AP EAMCET PYQs