Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA2011MathematicsQuadratic EquationActual

Let , be the roots of the equation (x-a)(x-b)=c, c 0 . Then the roots of the equation (x- )(x- )+c=0 are

Options

  1. Aa, c
  2. Bb, c
  3. Ca, b
  4. Da+b, a+c

Correct answer

C. a, b

Step-by-step solution

The given equation (x-a)(x-b)=c can be written as x^2-(a+b) x+(a b-c)=0 ...(i) , are the roots of the equation . array rl + & =a+b & =a b-c array ...(ii) If and are the roots of equation aligned (x- )(x- )+c & =0 x^2-( + ) x+( +c) & =0 + = + & =a+b aligned and . = +c=a b by (i i) Clearly, the roots and are a and b .

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