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3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient?
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3x²-x-4 find the zero of the following quadratic polynomial and verify...
Finding the Zero of the Quadratic Polynomial 3x² - x - 4
To find the zeros of the quadratic polynomial 3x² - x - 4, we need to set the polynomial equal to zero and solve for x.
Setting the Polynomial Equal to Zero:
3x² - x - 4 = 0
Factoring the Polynomial:
(3x + 4)(x - 1) = 0
Finding the Zeros:
Setting each factor to zero:
3x + 4 = 0 or x - 1 = 0
3x = -4 x = 1
x = -4/3
Therefore, the zeros of the quadratic polynomial are x = -4/3 and x = 1.
Relationship between Zeros and Coefficients:
The relationship between the zeros of a quadratic polynomial and its coefficients can be seen through Vieta's formulas. For a quadratic polynomial ax² + bx + c = 0 with zeros α and β, the relationship is as follows:
α + β = -b/a
αβ = c/a
In the case of the polynomial 3x² - x - 4, the sum of the zeros is (-1)/3 = -1/3 and the product of the zeros is -4/3. These values match the relationships given by Vieta's formulas, demonstrating the connection between the zeros and coefficients of the quadratic polynomial.
To find the zeros of the quadratic polynomial 3x² - x - 4, we need to set the polynomial equal to zero and solve for x.
Setting the Polynomial Equal to Zero:
3x² - x - 4 = 0
Factoring the Polynomial:
(3x + 4)(x - 1) = 0
Finding the Zeros:
Setting each factor to zero:
3x + 4 = 0 or x - 1 = 0
3x = -4 x = 1
x = -4/3
Therefore, the zeros of the quadratic polynomial are x = -4/3 and x = 1.
Relationship between Zeros and Coefficients:
The relationship between the zeros of a quadratic polynomial and its coefficients can be seen through Vieta's formulas. For a quadratic polynomial ax² + bx + c = 0 with zeros α and β, the relationship is as follows:
α + β = -b/a
αβ = c/a
In the case of the polynomial 3x² - x - 4, the sum of the zeros is (-1)/3 = -1/3 and the product of the zeros is -4/3. These values match the relationships given by Vieta's formulas, demonstrating the connection between the zeros and coefficients of the quadratic polynomial.
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3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient?
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3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient?.
3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 3x²-x-4 find the zero of the following quadratic polynomial and verify the relationship between the zeros and the coefficient?.
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