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1.Relation and Function
hard
વક્ર $f(x)=e^{8 x}-e^{6 x}-3 e^{4 x}-e^{2 x}+1, x \in R$,એ $x-$અક્ષને જ્યાં છેદે તે બિંદુઓની સંખ્યા $.........$ છે.
A
$2$
B
$4$
C
$6$
D
$8$
(JEE MAIN-2023)
Solution
Let $e ^{2 x }= t$
$\Rightarrow t^4-t^3-3 t^2-t+1=0$
$\Rightarrow t^2+\frac{1}{t^2}-\left(t+\frac{1}{t}\right)-3=0$
$\Rightarrow\left(t+\frac{1}{t}\right)^2-\left(t+\frac{1}{t}\right)-5=0$
$\Rightarrow t+\frac{1}{t}=\frac{1+\sqrt{21}}{2}$
Two real values of $t$.
Standard 12
Mathematics
