How many real solutions does the equation $x^7+14 x^5+16 x^3+30 x-560=0$ have?
How many real solutions does the equation $x^7+14 x^5+16 x^3+30 x-560=0$ have?
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7
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1
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3
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5
Solution
$
\begin{aligned}
& x^7+14 x^5+16 x^3+30 x-560=0 \\
& \text { Let } f(x)=x^7+14 x^5+16 x^3+30 x \\
& \Rightarrow f^{\prime}(x)=7 x^6+70 x^4+48 x^2+30>0 \forall x
\end{aligned}
$
$\therefore f(x)$ is an increasing function $\forall x$
Asked in: JEE Main 2008
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