If f ( x ) is a polynomial of least degree such that f ( r ) = r 1 , r = 1 , 2 , 3 , … 9 , then f ( 10 ) =

x f ( x ) − 1 = 0 has roots 1 , 2 , 3 ____ 9 x f ( x ) − 1 = A ( x − 1 ) ( x − 2 ) ____ x-9 Put x = 0 ⇒ A = 9 ! 1 Put x = 10 ⇒ 10 f ( 10 ) − 1 = 1 ⇒ f ( 10 ) = 5 1

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationTheory of equationsMedium2 minQB

MathematicsMediumsingle choice

If $f (x)$ is a polynomial of least degree such that $f (r) = \frac{1}{r}, r = 1, 2, 3, \dots 9$ , then $f (10) =$

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Answer:

Solution:

$x f (x) - 1 = 0$ has roots $1, 2, 3$ $____$ 9

$x f (x) - 1 = A (x - 1) (x - 2)$ $____$ x-9

Put $x = 0 \Rightarrow A = \frac{1}{9 !}$

Put $x = 10 \Rightarrow 10 f (10) - 1 = 1 \Rightarrow f (10) = \frac{1}{5}$

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Theory of equations

⏱ 2mℹ️ Source: QB

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