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Grade 12Algebra

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

bhavya chitikala

15 Years agoGrade 12

1 Answer

Jitender Singh

11 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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