Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202125 Aug 2021Evening ShiftMathematicsQuadratic EquationActual

Sum of the roots of the equation | array cccc x & 0 & 0 & 0 0 & 0 & 0 & 1 0 & x & 0 & 0 2 & 0 & x-1 & 0 array |- | array ccc 0 & x & 0 0 & 0 & x-1 2 & 2 & 0 array |=0 is

Options

  1. A2
  2. B3
  3. C1
  4. D5

Correct answer

B. 3

Step-by-step solution

| array cccc x & 0 & 0 & 0 0 & 0 & 0 & 1 0 & x & 0 & 0 2 & 0 & x-1 & 0 array |- | array ccc 0 & x & 0 0 & 0 & x-1 2 & 2 & 0 array |=0 On expanding first determinant along R₂ and second determinant along R_i aligned & 1 [x^2(x-1) ]-(-x)[-2(x-1)]=0 & x^3-x^2+x(-2 x+2)=0 & x^3-x^2-2 x^2+2 x=0 & x^3-3 x^2+2 x=0 & x (x^2-3 x+2 )=0 & x(x-1)(x-2)=0 & x=0,1 and 2 & aligned x=0,1 and 2 Sum of the roots =0+1+2=3

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

If is the common root of the quadratic equations x^2-5 x+4 a=0 , x^2-2 a x-8=0 , where a R , then the value of ^4- ^3+68 is 2025If , are the roots of x^2-5 x-6 =0 and , are the roots of x^2-5 x-6 =0 , then + + + = 2025If , , are the roots of the equation x ^3+ px ^2+ qx + r =0 , then ( + )( + )( + )= 2025Let f(x)=x^2+2 b x+2 c^2 and g(x)=-x^2-2 c x+b^2, x R . If b and c are nonzero real numbers such that f(x)> g(x) , then | c b | lies in the interval 2025If x ^2-4 ax +5+ a >0 for all x R whenever a ( , ) , then 4 + = 2025If , , are the roots of the equation x^3-12 x^2+k x-18=0 and one of them is thrice the sum of the other two roots, then ^2+ ^2+ ^2-k= 2025The polynomial equation of degree 5 whose roots are the roots of the equation x^5-3 x^4-x^3+11 x^2-12 x+4=0 each increased by 2, is 2025If the difference of the roots of the equation x^2-7 x+10=0 is same as the difference of the roots of the equation x ^2-17 x + k =0 , then a divisor of k is 2025 Full Quadratic Equation list All AP EAMCET PYQs