AP EAMCET202120 Aug 2021Morning ShiftMathematicsQuadratic EquationActual
If 2 , 1 , 1 are roots of the equation x 3 - 4 x 2 + 5 x - 2 = 0 , then the roots of x + 1 3 3 - 4 x + 1 3 2 + 5 x + 1 3 - 2 = 0
Options
- A7 3 , 4 3 , 4 3
- B5 3 , 2 3 , 2 3
- C- 5 3 , - 2 3 , - 2 3
- D- 7 3 , - 4 3 , - 4 3
Correct answer
B. 5 3 , 2 3 , 2 3
Step-by-step solution
If 2 , 1 , 1 are roots of the equation x 3 - 4 x 2 + 5 x - 2 = 0 Putting 2 ,   1 ,   1 in the equation we get: 2 3 + 4 × 2 2 + 5 × 2 - 2 = 0 ; 1 3 + 4 × 1 2 + 5 × 1 - 2 = 0 ; 1 3 + 4 × 1 2 + 5 × 1 - 2 = 0 ; To find the roots of second equation we will subtract 1 3 from the roots of the first equation, So, the roots are 2 - 1 3 ,   1 - 1 3 ,   1 - 1 3 ≡ 5 3 , 2 3 , 2 3 x + 1 3 3 - 4 x + 1 3 2 + 5 x + 1 3 - 2 = 0 Putting 5 3 , 2 3 , 2 3 in the equation we get 2