Q16 / 82 · NTA Abhyas (JEE Main) 2020 · Mathematics · Quadratic Equation

The quadratic equation whose roots are the arithmetic mean and the harmonic mean of the roots of the equation x2+7x-1=0 is

  • A
    14x2+14x-45=0
  • B
    45x2-14x+14=0
  • Correct answer
    C
    14x2+45x-14=0
  • D
    45x2+14x-45=0

Solution

Let, α,β are the roots of the equation x2+7x-1=0

⇒α+β=-7,αβ=-1

⇒A=α+β2=-72

and H=2αβα+β=2-1-7=27.
Now, equation whose roots are A and H is
x2-A+Hx+AH=0⇒x2-x-72+27+-7227=0
⇒x2+4514x-1=0⇒14x2+45x-14=0

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

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