Question

[ 1 ] check whether -3 and 3 are the zeroes of the polynomial x² - 9.

[ 2 ] Draw the graph of (i) y = 2x + 5, ( ii ) y = 2x - 5 ( iii ) y = 2x and find the point of intersection on x - axis. Is the x-coordinates of these points also the zero of the polynomial ?

[ 3 ] Draw the graphs of (i) y = x² - x - 6 ( ii ) y = 6 - x - x² and find zeroes in each case. What do you Notice?
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Answer 1

#1

• x² - 9 = 0
• x² = 9
• x = ± √9
• x = ± 3

Yes, -3 and 3 are zeroes of this polynomial

#2

See attached graphs

Zero's of a polynomial are the intersection of the graph with the x-axis.

They include coordinates as (x, 0), so the x-coordinates are zero's.

The attached shows the zero's.

#3

See attached graphs

Zero's of each polynomial are reflected in the graphs.

• () y = x² - x - 6 has zeros x = -2 and x = 3
• (ii) y = 6 - x - x² has zero's x = -3, x = 2