Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202317 May 2023Evening ShiftMathematicsQuadratic EquationActual

If ₁, ₂ and ₃ are the roots of x^3+3 x+2=0 , then ₁^5+ ₂^5+ ₃^5=

Options

  1. A-30
  2. B6
  3. C-6
  4. D30

Correct answer

D. 30

Step-by-step solution

Since, ₁, ₂ & ₃ are the roots of x^3+3 x+2=0 . aligned & ₁+ ₂+ ₃=0 & ₁ ₂+ ₂ ₃+ ₃ ₁=3 & ₁ ₂ ₃=-2 aligned Now, ₁^5+ ₂^5+ ₃^5= ₁^3 ₁^2+ ₂^3 ₂^2+ ₃^3 ₃^2 aligned & = (-3 ₁-2 ) ₁^2+ (-3 ₂-2 ) ₂^2+ (-3 ₃-2 ) ₃^2 & =-3 ₁^3-2 ₁^2-3 ₂^3-2 ₂^2-3 ₃^3-2 ₃^2 & =- (-3 ₁-2 )-3 (3 ₂-2 )-3 (3 ₃-2 )-2 ( ₁^2+ ₂^2+ ₃^2 ) & =9 ( ₁+ ₂+ ₃ )-2 [ ( ₁+ ₂+ ₃ )^2-2 ( ₂ ₁+ ₂ ₃ . . & =9 0-2 [0^2-2 (3) ]+18 & ₁^5+ ₂^5+ ₃^5=30 aligned

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