Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2024MathematicsQuadratic EquationActual

Under which one of the following conditions does the equation ( -1) x^2+( ) x+ =0 in x have a real root for [0, ] ?

Options

  1. A1- 0
  2. B1- 0
  3. C1- 0
  4. D1- 0

Correct answer

B. 1- 0

Step-by-step solution

For real roots ( )^2-4 ( -1) 0 Since, -1 1 and 0 for [0, ] So, it is only possible when, -1 0 .

Practice Quadratic Equation on Quantrex Academy →

More from Quadratic Equation

For a given k , what is the minimum value of x^2+kx+k^2 ? 2026If the highest degree coefficient is equal to 1 , then what is the total number of quadratic equations which are unchanged on squaring their roots ? 2026Let and be the roots of the quadratic equation x^2-2bx+c^2=0 where b , c are positive real numbers. Let A be the arithmetic mean of and ; and G be the geometric mean of and . What 2026Consider the following statements : I. x +x+1=0 has two irrational roots. II. 5 x -x-4=0 has two rational roots. Which of the statements given above is/are correct ? 2026For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such that f(1) = f(4) = 2 . Further, 2 is a root of f(x) = 0 . What is (a + b + c) equal to? 2025For the following two (02) items: Let and be the roots of the quadratic equation x^2 + ( _ 0.5 (a^2))x + ( _ 0.5 (a^2))^4 = 0 , where a^2 1 and _ 0.5 (a^2) > 0 . Further, ^2 = ( _ 2025For the following two (02) items: Let f(x) = ax^2 + bx + c be a quadratic polynomial such that f(1) = f(4) = 2 . Further, 2 is a root of f(x) = 0 . What is the other root of f(x) = 2025If one root of the equation x^2 - kx + k = 0 exceeds the other by 2 3 , then which one of the following is a value of k ? 2025 Full Quadratic Equation list All NDA PYQs