If f(x)= begincasesx2-1, 0

Question

If f(x)= begincasesx2-1, 0 < x < 2 2 x+3, 2 ≤ x < 3 endcases the quadratic equation whose roots are displaystyle lim x arrow 2- f (x) and displaystyle lim x arrow 2+ f (x) is (A) x2-14 x+49=0 (B) x2-6 x+9=0 (C) x2-10 x+21=0 (D) x2-7 x+8=0

Tardigrade Admin · Accepted Answer

α= displaystyle lim x arrow 2- f(x)= displaystyle lim x arrow 2 x2-1=3 β= displaystyle lim x arrow 2+ f(x)= displaystyle lim x arrow 2 2 x+3=7 x2-(α+β) x+α β=0 x2-10 x+21=0

Q. If $f (x) = {x^{2} - 1, 2 x + 3, 0 < x < 2 2 \leq x < 3$
the quadratic equation whose roots are $x \to 2^{-} lim f (x)$ and $x \to 2^{+} lim f (x)$ is

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

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

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

$x^{2} - 7 x + 8 = 0$

$α = x \to 2^{-} lim f (x) = x \to 2 lim x^{2} - 1 = 3$
$β = x \to 2^{+} lim f (x) = x \to 2 lim 2 x + 3 = 7$
$x^{2} - (α + β) x + α β = 0$
$x^{2} - 10 x + 21 = 0$

Q. If f(x)={x2−1,2x+3,​0<x<22≤x<3​ the quadratic equation whose roots are x→2−lim​f(x) and x→2+lim​f(x) is

x2−14x+49=0

x2−6x+9=0

x2−10x+21=0

x2−7x+8=0