Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
AP EAMCET20224 Jul 2022Evening ShiftMathematicsQuadratic EquationActual

The sum of all the real roots of the equation x - 2 2 + x - 2 - 2 = 0 is

Options

  1. A7
  2. B4
  3. C1
  4. DNone of these

Correct answer

B. 4

Step-by-step solution

Given: x - 2 2 + x - 2 - 2 = 0       . . . . 1 Putting y = x - 2 , then we can rewrite 1 as y 2 + y - 2 = 0 ⇒ y 2 + 2 y - y - 2 = 0 ⇒ y y + 2 - y + 2 = 0 ⇒ y - 1 y + 2 = 0 ⇒ y = 1 ,   - 2 Since, y ≥ 0 , so y = x - 2 = 1 ⇒ x - 2 = ±   1 ⇒ x = 3   o r   1 Required sum is = 3 + 1 = 4

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