Let f x - x 2-1-00- x -2 and 2 x -3-2 - x -3- The quadratic equation whose roots are lim X - 2- f x - and lim X - 2- f x A- x2-10 x-21-0B- x2-10 x-49-0C- x2-6 x-9-0D- x2-14 x-49-0

The correct option is A x2 10x+21=0 lim_x→2 0f(x), lim_x→2 0(x^2 1)=2^2 1=3 lim_x→2 0f(x), lim_x→2 0(2x+3)=2×2+3=7 ∴Required quadratic equation is x^2 10x+21=0 ...

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Standard X

Mathematics

Formation of a Quadratic Equation From It's Roots

Let f x = x 2...

Question

Let f(x) = $x^{2}$ -1, 0 0<x<2 and 2x+3, 2 $\leq$ x<3, The quadratic equation whose roots are ${lim}_{x \to 2^{-}} f (x), a n d {lim}_{x \to 2^{+}} f (x)$

x² -6x+9=0

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x²-10x+21=0

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x²-14x+49=0

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$x^2-10x+49=0$

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Solution

The correct option is B
x²-10x+21=0

${lim}_{x \to 2 - 0} f (x), {lim}_{x \to 2 - 0} (x^{2} - 1) = 2^{2} - 1 = 3 {lim}_{x \to 2 - 0} f (x), {lim}_{x \to 2 - 0} (2 x + 3) = 2 \times 2 + 3 = 7 ∴ Required quadratic equation is x^{2} - 10 x + 21 = 0 Hence (b)is the correct answer$

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Similar questions

Q. Let

f (x) = (\begin{matrix} x^{2} - 1, if 0 < x < 2 2 x + 3, if 2 \leq x < 3 \end{matrix}

, a quadratic equation whose roots are

lim x \to 2^{-} f (x) and lim x \to 2^{+} f (x)

Q. 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)

Q. 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)

I f f (x) = {\begin{matrix} x^{2} - 3, & 2 < x < 3 2 x + 5, & 3 < x < 4 \end{matrix}

, the equation whose roots are

lim x \to 3 - f (x)

and

lim x \to 3 + f (x) i s

Q. Let

A = {x \in R : x^{2} - | x | - 2 = 0}

and

B = {α + β, α β}

where

α, β

are real roots of the quadratic equation

x^{2} + | x | - 2 = 0 .

(a, b) \in A \times B,

then the quadratic equation whose roots are

a, b

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

The correct option is B x2-10x+21=0 limx→2−0f(x), limx→2−0(x2−1)=22−1=3limx→2−0f(x), limx→2−0(2x+3)=2×2+3=7∴Required quadratic equation is x2−10x+21=0Hence (b)is the correct answer

Let f(x) = $x^{2}$ -1, 0 0<x<2 and 2x+3, 2 $\leq$ x<3, The quadratic equation whose roots are ${lim}_{x \to 2^{-}} f (x), a n d {lim}_{x \to 2^{+}} f (x)$

The correct option is B
x²-10x+21=0

${lim}_{x \to 2 - 0} f (x), {lim}_{x \to 2 - 0} (x^{2} - 1) = 2^{2} - 1 = 3 {lim}_{x \to 2 - 0} f (x), {lim}_{x \to 2 - 0} (2 x + 3) = 2 \times 2 + 3 = 7 ∴ Required quadratic equation is x^{2} - 10 x + 21 = 0 Hence (b)is the correct answer$