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Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 3x² 5x - 2?
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Find the zeroes of the following quadratic polynomial and verify the r...
Zeroes of Quadratic Polynomial
Relationship between Zeroes and Coefficient
- The quadratic polynomial is given as 3x² + 5x - 2.
- To find the zeroes of the polynomial, we need to solve for x such that the polynomial is equal to zero.
- Thus, we have the equation 3x² + 5x - 2 = 0.
- We can solve this equation using the quadratic formula:
- x = (-b ± √(b² - 4ac)) / 2a
- Here, a = 3, b = 5, and c = -2.
- Substituting these values in the formula, we get:
- x = (-5 ± √(5² - 4(3)(-2))) / 2(3)
- Simplifying, we get:
- x = (-5 ± √49) / 6
- Thus, the zeroes of the quadratic polynomial are:
- x = (-5 + 7) / 6 = 1/3
- x = (-5 - 7) / 6 = -2
Relationship between Zeroes and Coefficient
- Let the zeroes of the quadratic polynomial be α and β.
- Then, the polynomial can be written as:
- 3x² + 5x - 2 = 3(x - α)(x - β)
- Expanding the right-hand side, we get:
- 3x² - 3(α + β)x + 3αβ
- Comparing the coefficients of the quadratic term, linear term, and constant term, we get:
- α + β = -5/3
- αβ = -2/3
- Now, substituting the values of α and β, we get:
- α + β = 1/3 - 2 = -5/3
- αβ = (1/3)(-2) = -2/3
- Thus, we have verified the relationship between the zeroes and the coefficient of the quadratic polynomial.
Community Answer
Find the zeroes of the following quadratic polynomial and verify the r...
3ײ+5×-2
3x²+2x-3×-2
x(3x +2 ) -1 ( 3x+2)
(x-1) (3x+2)
x=1 × = -2/3
alpha = 1 beta = -2/3
alpha + beta = -b/a
1 + -2/3 = -(+5/3)
-5/3 =-5/3
alpha × beta = c/ a
1× -2/3 = -2/3
-2/3 = -2/3
3x²+2x-3×-2
x(3x +2 ) -1 ( 3x+2)
(x-1) (3x+2)
x=1 × = -2/3
alpha = 1 beta = -2/3
alpha + beta = -b/a
1 + -2/3 = -(+5/3)
-5/3 =-5/3
alpha × beta = c/ a
1× -2/3 = -2/3
-2/3 = -2/3
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Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 3x² 5x - 2?
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Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 3x² 5x - 2? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 3x² 5x - 2? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient 3x² 5x - 2?.
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