Question

find zeroes and show them graphically . (i) 2+x-x^2​

Answer 1

Answer:

Factor of y=x

2 +2x+1

Plotting (−1,0),(0,1),(1,4) and joining them.

Here, the graph cuts x-axis at 0

solution

Answer 2

Step-by-step explanation:

Given: 2+x-x²

To find: Find zeros and show them graphically.

Solution:

Step 1: Write quadratic polynomial in standard form

$- {x}^{2} + x + 2$

Step 2: Split the middle term so as addition or subtraction of this term is equal to multiplication of first and last term

$- {x}^{2} + 2x - x + 2 \\ \\ \implies - x(x - 2) - 1(x - 2) \\ \\ \implies (x - 2)( - x - 1)$

Step 3: Find the zeros by equating factors to zero

$(x - 2)( - x - 1) = 0 \\ \\ either \\ \\ x - 2 = 0 \\ \\ x = 2 \\ \\o r \\ \\ - x - 1 = 0 \\ \\ - x = 1 \\ \\ x = - 1$

Step 4: Zeros of polynomial are -1 and 2.

Step 5:To graph the polynomial and locate zeros

put polynomial as shown

$y = - {x}^{2} + x + 2$

put different values of x and find values of y

$\begin{tabular}{|c|c|c|}\cline{1-7}x&y\\\cline{1-7}0&2\\\cline{1-7}1&2\\\cline{1-7}-1&0\\\cline{1-7}2&0\\\cline{1-7}-2&-4\\\cline{1-7}3&-4\\\cline{1-7}\end{tabular}$

Step 6: Locate these points and make a smooth curve,the curve intersect x-axis at two places are the zeros of polynomial.Zeros are plot with red colour.

Graph is attatched.

Final answer:

Zeros of polynomial are -1 and 2.

Hope it helps you.

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