Q41 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

If x is rational and 4x2+1x2+16x+1x-57=0,⁡ then the product of all possible values of x is

  • Correct answer
    A
    4
  • B
    3
  • C
    2
  • D
    1

Solution

Given equation,
4 x 2 + 1 x 2 + 1 6 x + 1 x - 5 7 = 0
Let, x+1x=y;  x 2 + 1 x 2 = y 2 - 2
⇒  4 y 2 + 1 6 y - 6 5 = 0
⇒  y=-132 or⁡ 52
When,  y = 5 2
x+1x=52⇒x=2 or 12
When, y=-132
⇒  x + 1 x = - 1 3 / 2
⇒  2 x 2 + 1 3 x + 2 = 0
⇒  x = - 1 3 ± 1 5 3 4
Since x is rational, x=2 or 1 2

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

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