Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET201822 Apr 2018Evening ShiftMathematicsQuadratic EquationActual

If and are the roots of the equation x^2-4 x+5=0 , then the quadratic equation whose roots are ^2+ and + ^2 is

Options

  1. Ax^2+10 x+34=0
  2. Bx^2-10 x+34=0
  3. Cx^2-10 x-34=0
  4. Dx^2+10 x-34=0

Correct answer

B. x^2-10 x+34=0

Step-by-step solution

Since, and are roots of the quadratic equation x^2-4 x+5=0 Now, ( ^2+ )+ ( + ^2 )= ( ^2+ ^2 )+( + ) aligned & =( + )^2-2 +( + ) & =16-10+4=10 aligned and ( ^2+ ) aligned & ( + ^2 )= ^3+ ^2 ^2+ + ^3 & = ^3+ ^3+ ( +1) & =( + ) ( ^2+ ^2- )+ ( +1) & =( + ) [( + )^2-3 ]+ ( +1) & =4[16-15]+5(5+1) & =4+30=34 aligned So, the quadratic equation whose roots are ( ^2+ ) and ( + ^2 ) is aligned x^2- ( ^2+ + + ^2 ) x+ ( ^2+ ) ( + ^2 ) & =0 x^2-10 x+34 & =0 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