SECTION - III
(2) Each question carries 6 marks.
13. Draw the graph of the polynomial and find zeroes of the polyn
from the graph.
14. Find the mode of the following data.

Ask by Marsh Hardy. in India

Mar 27,2025

Question

SECTION - III (2) Each question carries 6 marks. 13. Draw the graph of the polynomial $$ p(x)=x^{2}+2 x-3 $$ and find zeroes of the polyn from the graph. 14. Find the mode of the following data.

UpStudy AI · Accepted Answer

### Question 13

1. **Factorize the Polynomial**  
   We are given  
   $$
   p(x)=x^{2}+2x-3.
   $$  
   To factorize, we look for two numbers whose product is $$-3$$ and whose sum is $$2$$. These numbers are $$3$$ and $$-1$$, so we can write  
   $$
   x^{2}+2x-3 = (x+3)(x-1).
   $$

2. **Find the Zeros**  
   Setting $$p(x)=0$$ gives  
   $$
   (x+3)(x-1)=0.
   $$  
   Therefore, the zeros are  
   $$
   x+3=0 \quad \Rightarrow \quad x=-3,
   $$  
   and  
   $$
   x-1=0 \quad \Rightarrow \quad x=1.
   $$

3. **Determine Key Points for the Graph**  
   - **Vertex:**  
     The vertex of a parabola given by $$ax^2+bx+c$$ is at  
     $$
     x=-\frac{b}{2a}.
     $$  
     Here, $$a=1$$ and $$b=2$$, so  
     $$
     x=-\frac{2}{2}= -1.
     $$  
     Plugging $$x=-1$$ into $$p(x)$$:  
     $$
     p(-1)= (-1)^2+2(-1)-3 = 1-2-3 = -4.
     $$  
     So, the vertex is at $$(-1, -4)$$.

- **Intercepts:**  
     - $$x$$-intercepts (zeros): $$(-3, 0)$$ and $$(1, 0)$$.  
     - $$y$$-intercept: When $$x=0$$,  
       $$
       p(0)=0^2+2(0)-3=-3.
       $$  
       So, the $$y$$-intercept is at $$(0,-3)$$.

4. **Sketching the Graph**  
   The graph is a parabola opening upwards (since $$a=1>0$$). It has:
   - A vertex at $$(-1,-4)$$.
   - Zeros at $$x=-3$$ and $$x=1$$.
   - A $$y$$-intercept at $$(0,-3)$$.

A rough sketch would show a curved "U" shape with the vertex at $$(-1, -4)$$ and passing through the points $$(-3, 0)$$, $$(1, 0)$$, and $$(0, -3)$$.

### Question 14

The problem asks: "Find the mode of the following data."  
However, the data values are not provided. The mode is defined as the value that occurs most frequently in a data set. Without the specific data, we cannot determine the mode.

Please provide the data set so that we can compute the mode.
### Question 13 - **Zeros of the Polynomial $$ p(x) = x^{2} + 2x - 3 $$:** The zeros are $$ x = -3 $$ and $$ x = 1 $$. - **Graph of the Polynomial:** The graph is a parabola opening upwards with: - Vertex at $$(-1, -4)$$ - Zeros at $$(-3, 0)$$ and $$(1, 0)$$ - $$y$$-intercept at $$(0, -3)$$ ### Question 14 Cannot determine the mode as the data set is not provided.

SECTION - III
(2) Each question carries 6 marks.
13. Draw the graph of the polynomial and find zeroes of the polyn
from the graph.
14. Find the mode of the following data.

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SECTION - III (2) Each question carries 6 marks. 13. Draw the graph of the polynomial and find zeroes of the polyn from the graph. 14. Find the mode of the following data.