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A real number is called zeros of the polynomial p(x) if _________
- a)p(α) = 4
- b)p(α) = 1
- c)p(α) ≠ 0
- d)p(α) = 0
Correct answer is option 'D'. Can you explain this answer?
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A real number is called zeros of the polynomial p(x) if _________a)p(&...
A number is called zero of polynomial when it satisfies the equation of the polynomial.
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A real number is called zeros of the polynomial p(x) if _________a)p(&...
Definition of Zeros of a Polynomial:
Zeros of a polynomial are the real numbers that make the polynomial equal to zero when substituted for the variable.
Explanation of the Correct Answer:
Option D: p(α) = 0
This option is the correct answer because the zeros of a polynomial are the values of the variable that make the polynomial equal to zero. In other words, if a real number α is a zero of the polynomial p(x), then p(α) = 0. This is a fundamental property of zeros of polynomials.
Therefore, the correct statement to define zeros of a polynomial is p(α) = 0.
Understanding the Other Options:
- Option A: p(α) = 4
This statement does not define the zeros of the polynomial. Zeros of a polynomial are the values that make the polynomial equal to zero, not any other constant.
- Option B: p(α) = 1
Similarly, this statement does not define the zeros of the polynomial. Zeros are the values that make the polynomial equal to zero, not 1.
- Option C: p(α) ≠ 0
This statement does not accurately define the zeros of the polynomial. Zeros are the values that make the polynomial equal to zero, not any value other than zero.
In Conclusion:
The correct definition of zeros of a polynomial is when the polynomial evaluated at a real number α results in p(α) = 0. This is a fundamental concept in algebra and is crucial in understanding the roots of polynomial functions.
Zeros of a polynomial are the real numbers that make the polynomial equal to zero when substituted for the variable.
Explanation of the Correct Answer:
Option D: p(α) = 0
This option is the correct answer because the zeros of a polynomial are the values of the variable that make the polynomial equal to zero. In other words, if a real number α is a zero of the polynomial p(x), then p(α) = 0. This is a fundamental property of zeros of polynomials.
Therefore, the correct statement to define zeros of a polynomial is p(α) = 0.
Understanding the Other Options:
- Option A: p(α) = 4
This statement does not define the zeros of the polynomial. Zeros of a polynomial are the values that make the polynomial equal to zero, not any other constant.
- Option B: p(α) = 1
Similarly, this statement does not define the zeros of the polynomial. Zeros are the values that make the polynomial equal to zero, not 1.
- Option C: p(α) ≠ 0
This statement does not accurately define the zeros of the polynomial. Zeros are the values that make the polynomial equal to zero, not any value other than zero.
In Conclusion:
The correct definition of zeros of a polynomial is when the polynomial evaluated at a real number α results in p(α) = 0. This is a fundamental concept in algebra and is crucial in understanding the roots of polynomial functions.
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A real number is called zeros of the polynomial p(x) if _________a)p(α) = 4b)p(α) = 1c)p(α) ≠ 0d)p(α) = 0Correct answer is option 'D'. Can you explain this answer?
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