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let f be a continuous functiondefinewd on [-2009,+2009] such that f(x) is irrational for each xbelongs to[-2009,2009] &f(0)=2+root 2+root5. the equation f(2002)x^2 +2f(0)x+f(2009)=0 has? A)ONLY RATIONAL ROOTS B)ONLY IRRATIONAL ROOTS C)ONE RAT&ONE IRR D)IMAGINARY ROOTS


  • let f be a continuous functiondefinewd on [-2009,+2009] such that f(x) is irrational for each xbelongs to[-2009,2009] &f(0)=2+root 2+root5.  the equation f(2002)x^2 +2f(0)x+f(2009)=0  has?                  A)ONLY RATIONAL ROOTS

  • B)ONLY IRRATIONAL ROOTS

  • C)ONE RAT&ONE IRR

  • D)IMAGINARY ROOTS

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello Student,
Please find answer to your question below
f is continuous on the interval & rational on the [-2009, 2009].
The result of this is that f is constant.
f(0) = 2 + \sqrt{2} + \sqrt{5}
Since f is constant we have
f(2002) = f(2009) = 2+\sqrt{2}+\sqrt{5}
So the equation,
f(2002)x^{2} + 2f(0)x + f(2009) = 0
f(0)(x^{2} + 2x + 1) = 0
x^{2} + 2x + 1 = 0
(x+1)^{2} = 0
x = -1, -1
So both roots are rational.

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