Class X Session 2023-24 Question 2

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 MATH SAMPLE QUESTION PAPER

Class X Session 2023-24

MATHEMATICS STANDARD (Code No.041)

Question 2

The given linear polynomial y = f(x) has 

(a) 2 zeros 

(b) 1 zero and the zero is ‘3’ 

(c) 1 zero and the zero is ‘4’ 

(d) No zero  


Explanation :

A linear polynomial has the form y=mx+c, where m is the slope and c is the y-intercept. Since it's a linear polynomial, it represents a straight line.

The number of zeros of a linear polynomial is the number of points where it intersects the x-axis.  If the slope (m) is not zero, the line will intersect the x-axis at exactly one point, unless it is parallel to the x-axis, in which case it will never intersect the x-axis.

If the slope is zero ( m= 0 ) the line will be horizontal and parallel to the x-axis. In this case, it will intersect the x-axis only if the y-intercept 

Given the polynomial: Y=f(X), if it's linear, it will have either:

  • 1 zero if the slope (m) is not zero, and the zero is the x-coordinate of the point where it intersects the x-axis.
  • No zero if the slope (m) is zero and the y-intercept (c) is not zero.
Based on the options given, we can say:
  • No zero if the linear polynomial is of the form y=c (a horizontal line where c is a constant).
  • 1 zero and the zero is '3' if the linear polynomial is of the form y=mx+c and it intersects the x-axis at 3, x=3.
  • 1 zero and the zero is '4' if the linear polynomial is of the form y=mx+c and it intersects the x-axis at 4, x=4

Guess the Option and comment below  👇

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