Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET202318 May 2023Morning ShiftMathematicsQuadratic EquationActual

If one root of the equation x^3-6 x^2+3 x+10=0 is the average of the other two, then the sum of fourth powers of the roots of the equation is

Options

  1. A642
  2. B643
  3. C644
  4. D645

Correct answer

A. 642

Step-by-step solution

Let , and are the roots of x^3-6 x^2+3 x+10=0 Also, let = + 2 2 = + +2+ =6 + =4 ...(i) Also, =-10 =-5 Now, - = ( + )^2-4 = 16+20 = 6 aligned & Equation (i) + (ii) & 2 =10 =5 & from (i) =4-5=-1 & Now, ^4+ ^4+ ^4=5^4+2^4+(-1)^4=625+16+1 & =642 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