Class 10 Exam > Class 10 Questions > If the point (5,0) , (0-2) and (3,6) lie on t...
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If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?
- a)5
- b)6
- c)not defined
- d)-2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial ...
Explanation:
Since, a zero of a polynomial always lies on the x-axis as a point. In the given question the point (5,0) is a point that lies on x-axis, so its corresponding x value represents zero of the polynomial.
Therefore, 5 is the zero of the polynomial.
Hence, the correct option is A.
You can know more about Geometrical Meaning of the Zeroes of a Polynomial through the document:
Most Upvoted Answer
If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial ...
The point at which the The graph cuts X- axis is its zero.So in this Out of all options 5 is abscissa or X coordinate. Hence it is zero of given polynomial
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Community Answer
If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial ...
To determine which of the given options is a zero of the polynomial, we need to find the equation of the polynomial that passes through the given points.
The equation of a polynomial can be expressed in the form:
P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
where n is the degree of the polynomial and a_n, a_(n-1), ..., a_2, a_1, a_0 are coefficients.
To find the equation of the polynomial, we can use the given points to set up a system of equations.
1. Plug in the coordinates of the first point (5, 0):
0 = a_n(5)^n + a_(n-1)(5)^(n-1) + ... + a_2(5)^2 + a_1(5) + a_0
2. Plug in the coordinates of the second point (0, -2):
-2 = a_n(0)^n + a_(n-1)(0)^(n-1) + ... + a_2(0)^2 + a_1(0) + a_0
3. Plug in the coordinates of the third point (3, 6):
6 = a_n(3)^n + a_(n-1)(3)^(n-1) + ... + a_2(3)^2 + a_1(3) + a_0
Solving this system of equations will give us the coefficients of the polynomial, which will allow us to determine the zeros.
Since the system of equations is not provided, we cannot solve it directly. Therefore, we cannot determine which option is a zero of the polynomial based on the given information.
Hence, the correct answer cannot be determined from the information given. The correct answer is not provided among the given options.
The equation of a polynomial can be expressed in the form:
P(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_2x^2 + a_1x + a_0
where n is the degree of the polynomial and a_n, a_(n-1), ..., a_2, a_1, a_0 are coefficients.
To find the equation of the polynomial, we can use the given points to set up a system of equations.
1. Plug in the coordinates of the first point (5, 0):
0 = a_n(5)^n + a_(n-1)(5)^(n-1) + ... + a_2(5)^2 + a_1(5) + a_0
2. Plug in the coordinates of the second point (0, -2):
-2 = a_n(0)^n + a_(n-1)(0)^(n-1) + ... + a_2(0)^2 + a_1(0) + a_0
3. Plug in the coordinates of the third point (3, 6):
6 = a_n(3)^n + a_(n-1)(3)^(n-1) + ... + a_2(3)^2 + a_1(3) + a_0
Solving this system of equations will give us the coefficients of the polynomial, which will allow us to determine the zeros.
Since the system of equations is not provided, we cannot solve it directly. Therefore, we cannot determine which option is a zero of the polynomial based on the given information.
Hence, the correct answer cannot be determined from the information given. The correct answer is not provided among the given options.
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If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?a)5b)6c)not definedd)-2Correct answer is option 'A'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?a)5b)6c)not definedd)-2Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the point (5,0) , (0-2) and (3,6) lie on the graph of a polynomial . Then which of the following is a zero of the polynomial?a)5b)6c)not definedd)-2Correct answer is option 'A'. Can you explain this answer?.
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