Question

Draw the graphs of the given polynomial and find the zeros. Justify the answers.
(i) p(x) = x² – x – 12 (ii) p(x) = x² – 6x + 9
(iii) p(x) = x² – 4x + 5 (iv) p(x) = x² + 3x – 4
(v) p(x) = x² – 1

Answer 1

Answer:

The number of zeros of the polynomial function is determined by the number of points it intersects the x-axis

(i) p(x) = x² – x – 12

Here, the number of zeros are 2 and the zeros are the points where the graph of the polynomial intersects the x-axis.

Zeros are : (-3 , 0) and (4 , 0)

(ii) p(x) = x² – 6x + 9

Here, the graph of the polynomial intersects the x-axis at one point.

Zeros are : (3 , 0)

(iii) p(x) = x² – 4x + 5

Here, the graph of the polynomial do not intersects the x-axis at any point so the given polynomial has no real zeros

(iv) p(x) = x² + 3x – 4

Here, the graph of the polynomial intersects the x-axis at 2 points.

Zeros are : (-4 , 0) and (1 , 0)

(v) p(x) = x² – 1

Here, the graph of the polynomial intersects the x-axis at 2 points.

Zeros are : (-1 , 0) and (1 , 0)

Answer 2

polynomial the zeros

p(x)= X2 -x-12