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If p(x) is a polynomial of degree one and p(y) = 0, then y is said to be
- a)Zero of p(x)
- b)Value of p(x)
- c)Constant of p(x)
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If p(x) is a polynomial of degree one and p(y) = 0, then y is said to ...
Let p(x) = mx + n
Put x = y
p(y) = my + n = 0
So, y is zero of p(x).
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If p(x) is a polynomial of degree one and p(y) = 0, then y is said to ...
Explanation:
For a polynomial of degree one, the general form is given by p(x) = ax + b, where 'a' and 'b' are constants.
To understand why option 'A' is the correct answer, let's consider the given condition p(y) = 0.
Zero of p(x):
A zero (or root) of a polynomial is a value of the variable that makes the polynomial equal to zero. In other words, if p(x) = 0, then 'x' is a zero of p(x).
In this case, p(y) = 0, which means that the polynomial is equal to zero when x = y. So, 'y' is a zero of p(x).
Therefore, option 'A' is the correct answer.
Other options:
Value of p(x):
The value of a polynomial at a particular point is obtained by substituting that point into the polynomial. In this case, p(y) represents the value of the polynomial at the point x = y. However, we are not given any information about the value of p(x) or y, so option 'B' is incorrect.
Constant of p(x):
The constant term of a polynomial is the term that does not have any variable associated with it. In the given polynomial p(x) = ax + b, the constant term is 'b'. However, we are not given any information about the constant term or its relation to y, so option 'C' is incorrect.
Conclusion:
Based on the given condition p(y) = 0, the correct answer is option 'A' - y is a zero of p(x).
For a polynomial of degree one, the general form is given by p(x) = ax + b, where 'a' and 'b' are constants.
To understand why option 'A' is the correct answer, let's consider the given condition p(y) = 0.
Zero of p(x):
A zero (or root) of a polynomial is a value of the variable that makes the polynomial equal to zero. In other words, if p(x) = 0, then 'x' is a zero of p(x).
In this case, p(y) = 0, which means that the polynomial is equal to zero when x = y. So, 'y' is a zero of p(x).
Therefore, option 'A' is the correct answer.
Other options:
Value of p(x):
The value of a polynomial at a particular point is obtained by substituting that point into the polynomial. In this case, p(y) represents the value of the polynomial at the point x = y. However, we are not given any information about the value of p(x) or y, so option 'B' is incorrect.
Constant of p(x):
The constant term of a polynomial is the term that does not have any variable associated with it. In the given polynomial p(x) = ax + b, the constant term is 'b'. However, we are not given any information about the constant term or its relation to y, so option 'C' is incorrect.
Conclusion:
Based on the given condition p(y) = 0, the correct answer is option 'A' - y is a zero of p(x).
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If p(x) is a polynomial of degree one and p(y) = 0, then y is said to bea)Zero of p(x)b)Value of p(x)c)Constant of p(x)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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