Q47 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

If the graph of the function y=a-b2x2+2a+b-2cx+1 ∀a≠b is strictly above the x-axis, then

  • A
    a<b<c
  • Correct answer
    B
    a<c<b
  • C
    b<a<c
  • D
    c<b<a

Solution

D=B2-4AC
=2a+b-2c2-4a-b2
=4a+b-2c2-a-b2
=4a+b-2c-a+ba+b-2c+a-b
=42b-2c2a-2c
=16b-ca-c
=16c-bc-a
If c lies between a and b, then D is negative. Hence, the roots will be imaginary and the graph will be entirely above the x-axis as the coefficient of x2 is positive.

Hence, the correct answer is option: 'B'.

More Quadratic Equation Questions