Let α , β ( a

Question

Let α , β ( a < b ) be the roots of the equation a x 2 + b x + c = 0 . If lim x → m ​ a x 2 + b x + c ∣ a x 2 + b x + c ∣ ​ = 1 , then

TestHub · Accepted Answer

According to the given condition, we have

$a m^{2} + bm + c = a m^{2} + bm + c$

i.e. $a m^{2} + bm + c > 0$

$\Rightarrow$ if $a < 0$ , the $m$ lies in $(α, β)$

and if $a > 0$ , then $m$ does not lies in $(α, β)$

Hence, option ( c) is correct, since

$\frac{∣ a ∣}{a} = 1 \Rightarrow a > 0$

And in that case $m$ does not lie in $(α, β)$ .

Mathematics - Quadratic Equation Question with Solution | TestHub