(Q5)Draw the graphs of the given polynomial and find the zeros justify the answer. p(x) = x2 -x -12

Answer:

Given polynomial p(x)=x2-x-12.

List of values of p(x):

x -3 -2 -1 0 1 2 3 4
x2 4 0 1 9
x -3 -2 -1 0 1 2 3 4
x2-x 6 0 0 2
12 12 12 12 12 12 12 12 12
p(x) 0 -6 -10 -12 -12 -10 -6 0
(x,y) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , ) ( , )

Now,lets locate the points listed above on a graph paper

Result:We observe that the graph cuts the X - axis at(-3,0)and (4,0).

so, the zeros of the polynomial are -3 and 4.

justification:

Given:p(x)=x2-x-12=0

x2-4x+3x-12=0

x(x-)+3(x-)=0

(x-)(x+3=0)

x-=0 and x+3=0

x=and x=-3