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Most Important Selected Qs for JEE AdvancedMathematicsCircle

If (a, 0) is a point on a diameter of the circle x^2+y^2=4 , then the equation x^2-6 x-a^2=0 has -

Options

  1. Aexactly one real root in (-1,0]
  2. Bdistinct roots greater than -1
  3. Cexactly one real root in [3,7]
  4. Ddistinct roots less than 7

Correct answer

D. distinct roots less than 7

Step-by-step solution

Let f(x)=x^2-6 x-a^2 and as (a, 0) lies on the diameter of the circle so maximum value of a ^2 can be 4 Now array ll & f(-1)=1+6- a ^2 0 & f(0)=- a ^2 0 & f(3)=9-18- a ^2 0 & f(7)=49-42- a ^2 0 array so the equation x^2-6 x-a^2=0 has one root between -1 and 0 & one root betwen 3 and 7.

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