Let f x -x2-1 -0- x- 2 2x-3- 2- x- 3The quadratic equation whose roots are limx- 2-f x and limx- 2-f x is

The correct option is C x^2 10x+21=0 lim _ x→ 2 0 f( x ) =lim _ x→ 2 0 x^ 2 1=3 lim _ x→ 2+0 f( x ) =lim _ x→ 2+0 2x+3=7 Then equation whose ...

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Standard XII

Mathematics

Algebra of Limits

Let f x =x2...

Question

Let $f (x) = {\begin{matrix} x^{2} - 1; 0 < x < 2 2 x + 3; 2 \leq x < 3 \end{matrix}$
The quadratic equation whose roots are $lim x \to 2^{-} f (x)$ and $lim x \to 2^{+} f (x)$ is

x^{2} - 6 x + 9 = 0

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x^{2} - 10 x + 21 = 0

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x^{2} - 14 x + 49 = 0

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none of these

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Solution

The correct option is C $x^{2} - 10 x + 21 = 0$
${lim}_{x \to 2 - 0} f (x) = {lim}_{x \to 2 - 0} x^{2} - 1 = 3 {lim}_{x \to 2 + 0} f (x) = {lim}_{x \to 2 + 0} 2 x + 3 = 7$
Then equation whose roots are $3, 7$
$x^{2} - (3 + 7) x + (3 \times 7) = 0 \Rightarrow x^{2} - 10 x + 21 = 0$

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Let f(x)={x2−1;0<x<22x+3;2≤x<3The quadratic equation whose roots are limx→2−f(x) and limx→2+f(x) is

The correct option is C x2−10x+21=0limx→2−0f(x)=limx→2−0x2−1=3limx→2+0f(x)=limx→2+02x+3=7Then equation whose roots are 3,7x2−(3+7)x+(3×7)=0⇒x2−10x+21=0

Let $f (x) = {\begin{matrix} x^{2} - 1; 0 < x < 2 2 x + 3; 2 \leq x < 3 \end{matrix}$
The quadratic equation whose roots are $lim x \to 2^{-} f (x)$ and $lim x \to 2^{+} f (x)$ is

The correct option is C $x^{2} - 10 x + 21 = 0$
${lim}_{x \to 2 - 0} f (x) = {lim}_{x \to 2 - 0} x^{2} - 1 = 3 {lim}_{x \to 2 + 0} f (x) = {lim}_{x \to 2 + 0} 2 x + 3 = 7$
Then equation whose roots are $3, 7$
$x^{2} - (3 + 7) x + (3 \times 7) = 0 \Rightarrow x^{2} - 10 x + 21 = 0$