Question:
The number of points, where the curve y = x5 – 20x3 + 50x + 2 crosses the x-axis, is _____.
The number of points, where the curve y = x5 – 20x3 + 50x + 2 crosses the x-axis, is _____.
Updated On: Feb 20, 2026
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Correct Answer: 5
Solution and Explanation
We are given the function \( y = x^5 - 20x^3 + 50x + 2 \). To find the points where the curve crosses the x-axis, we need to solve for \( y = 0 \).
\includegraphics[width=0.75\linewidth]{5.png}
\[
\frac{dy}{dx} = 5x^4 - 60x^2 + 50 = 5x^4 - 12x^2 + 10
\]
We solve:
\[
\frac{dy}{dx} = 0 \quad \Rightarrow \quad x^4 - 12x^2 + 10 = 0
\]
Solving for \( x^2 \), we find:
\[
x^2 = 6 \pm \sqrt{26} \quad \Rightarrow \quad x^2 \approx 6 \pm 5.1
\]
Thus:
\[
x \approx \pm 3.3, \pm 0.95
\]
Therefore, the number of points where the curve cuts the x-axis is 5.
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