Class 10 Exam > Class 10 Questions > If p(x) is a polynomial of degree one and p(a...
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If p(x) is a polynomial of degree one and p(a) = 0, then a 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(a) = 0, then a is said to ...
Understanding Zero of a Polynomial
When we say that p(x) is a polynomial of degree one, it can be expressed in the form:
p(x) = mx + b,
where m is the slope and b is the y-intercept.
When we find that p(a) = 0, we are essentially finding the value of x for which the polynomial equals zero.
Definition of Zero of a Polynomial
- A zero of a polynomial is a value of x that makes the polynomial equal to zero.
- In this case, since p(a) = 0, 'a' is the value at which the polynomial intersects the x-axis.
Why Option A is Correct
- Since p(a) = 0, it directly indicates that 'a' is a solution to the equation p(x) = 0.
- Therefore, 'a' is indeed referred to as a "zero" of the polynomial p(x).
Other Options Explained
- Option B: Value of p(x)
This is incorrect because p(a) = 0 indicates the value of the polynomial at 'a', not 'a' itself.
- Option C: Constant of p(x)
This option is misleading since there is no constant term being referred to here; it's about the root or zero of the polynomial.
- Option D: None of the above
This is incorrect as we have already established that 'a' is indeed a zero of p(x).
In summary, when p(a) = 0 for a polynomial p(x) of degree one, 'a' is correctly termed as a zero of p(x), confirming that option A is the right answer.
When we say that p(x) is a polynomial of degree one, it can be expressed in the form:
p(x) = mx + b,
where m is the slope and b is the y-intercept.
When we find that p(a) = 0, we are essentially finding the value of x for which the polynomial equals zero.
Definition of Zero of a Polynomial
- A zero of a polynomial is a value of x that makes the polynomial equal to zero.
- In this case, since p(a) = 0, 'a' is the value at which the polynomial intersects the x-axis.
Why Option A is Correct
- Since p(a) = 0, it directly indicates that 'a' is a solution to the equation p(x) = 0.
- Therefore, 'a' is indeed referred to as a "zero" of the polynomial p(x).
Other Options Explained
- Option B: Value of p(x)
This is incorrect because p(a) = 0 indicates the value of the polynomial at 'a', not 'a' itself.
- Option C: Constant of p(x)
This option is misleading since there is no constant term being referred to here; it's about the root or zero of the polynomial.
- Option D: None of the above
This is incorrect as we have already established that 'a' is indeed a zero of p(x).
In summary, when p(a) = 0 for a polynomial p(x) of degree one, 'a' is correctly termed as a zero of p(x), confirming that option A is the right answer.
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Community Answer
If p(x) is a polynomial of degree one and p(a) = 0, then a is said to ...
If p(x) is a polynomial of degree one, it can be written as:
p(x) = mx + c
where m and c are constants, and m ≠ 0.
Given that p(a) = 0, substituting x = a into p(x):
p(a) = m(a) + c = 0
This equation implies that a is a root or zero of the polynomial p(x), as it satisfies p(a) = 0.
Hence, the correct answer is:
A: Zero of p(x)
p(x) = mx + c
where m and c are constants, and m ≠ 0.
Given that p(a) = 0, substituting x = a into p(x):
p(a) = m(a) + c = 0
This equation implies that a is a root or zero of the polynomial p(x), as it satisfies p(a) = 0.
Hence, the correct answer is:
A: Zero of p(x)
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