The number of positive roots of the function $f(x)$ shown below in the range $0 < x < 6$ is ____.
Step 1: Understand what is asked
Positive roots are the values of $x$ where the graph of $f(x)$ cuts or touches the $x$-axis in the interval $0 < x < 6$.
Step 2: Inspect the graph in the interval $0 < x < 6$
From the plot:
The curve starts above the $x$-axis near $x = 0$.
It crosses the $x$-axis once near $x \approx 1$.
It goes negative, then crosses upward near $x \approx 3$.
It reaches a local maximum and then crosses downward again near $x \approx 5$.
Each crossing corresponds to one real root.
Step 3: Count the roots
Number of $x$-axis crossings in $0 < x < 6$:
$= 3$
Final Answer:
$\boxed{3}$
Important Questions from Polynomial Roots
The product of the roots of the equation $x^4 + 1 = 0$ is _________ (answer in integer).
- If a, b, and c are the roots of $2x^3 – 3x^2 + px – 1 = 0$ and sum of the two roots is 1, the value of p is:
- Let $r$ be a root of the equation $x^2 + 2x + 6 = 0$.
Then the value of the expression $(r + 2)(r + 3)(r + 4)(r + 5)$ is - Solution of $f(x) = x^4 + 2x^3 - 4x^2 + 3x - 1 = 0$ is
The smallest positive root of the equation
$x^5 - 5x^4 - 10 x^3 + 50 x^2 + 9 x - 45 = 0$
lies in the range
