Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202123 Aug 2021Morning ShiftMathematicsQuadratic EquationActual

If , and are roots of the equation x^3+4 x-19=0 . Then, the value of ^3 19-4 + ^3 19-4 + ^3 19-4 is equal to

Options

  1. A0
  2. B3
  3. C-3
  4. D2

Correct answer

B. 3

Step-by-step solution

, and are roots of x^3+4 x-19=0 Then, + + =0 aligned + + & =4 & =19 aligned =19 From Eq. (ii), ( + )+ =4 gathered (- )+ =4 - ^2+ 19 =4 - ^3+19=4 gathered [using Eq. (i)] [using Eq. (iii)] or ^3=19-4 This gives ^3 19-4 =1 Similarly, from Eq. (ii), aligned & ( + )+ =4 & (- )+ =4 & - ^2+ 19 =4 & ^3=19-4 & ^3 19-4 =1 & aligned And, from Eq. (ii) array r ( + )+ =4 (- )+ 19 =4 array ^3 19-4 =1 Adding Eqs.(iv), (v) and (vi), we get ^3 19-4 + ^3 19-4 + ^3 19-4 =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