Question

Analytically decide, at how many points does the graphs of the following equations cross the $x$-axis
i. $y=5$
ii. $3x-27y=-27$
iii. $x^2=0$

• A. (i) zero
  (ii) one
  (iii) one
• B. (i) zero
  (ii) one
  (iii) zero
• C. (i) one
  (ii) one
  (iii) two
• D. (i) zero
  (ii) zero
  (iii) zero

Answer 1

The correct option is B (i) zero

(ii) one
(iii) zero
i. $y=5$
Since the given line is parallel to $x$-axis it will never cut the $x$-axis

ii. $3x-27y=-27$
Since the slope of the given line is not zero. It will cut the $x$-axis at one point

iii.This curve will touch the $x$-axis but never cut it.