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X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient?
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X square - 2x - 8 find the zeros of the following quadratic polynomial...
Finding Zeros of the Quadratic Polynomial
- To find the zeros of the quadratic polynomial x^2 - 2x - 8, we need to set the polynomial equal to zero and solve for x.
- The equation x^2 - 2x - 8 = 0 can be factored as (x - 4)(x + 2) = 0.
- Setting each factor to zero gives us x - 4 = 0 and x + 2 = 0.
- Solving these equations, we find x = 4 and x = -2.
Verifying Relationship between Zeros and Coefficients
- The relationship between the zeros of a quadratic polynomial and its coefficients is given by Vieta's formulas.
- Vieta's formulas state that for a quadratic polynomial ax^2 + bx + c = 0 with zeros p and q, the sum of the zeros is p + q = -b/a and the product of the zeros is pq = c/a.
- In our case, the sum of the zeros is 4 + (-2) = -b/a = 2, and the product of the zeros is 4 * (-2) = c/a = -8.
- Therefore, the relationship between the zeros 4 and -2 and the coefficients -2 and -8 of the quadratic polynomial x^2 - 2x - 8 is verified by Vieta's formulas.
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X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient?
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X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient?.
X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for X square - 2x - 8 find the zeros of the following quadratic polynomial and verifying relationship between the zeros and coefficient?.
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