find the zeroes of the quadratic polynomial 3x^2 - x - 4 and verify the relationship between the zeroes and the coefficient . answers bta jaldi
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Answer:
-1 and 4/3 are the zeroes of the given polynomial.
Step-by-step explanation:
Given polynomial,
3x² - x - 4
x² coefficeint = 3
x coefficient = -1
constant term = -4
- Finding the zeroes : (by factorization)
3x² - x - 4 = 0
3x² + 3x - 4x - 4 = 0
3x(x + 1) - 4(x + 1) = 0
(x + 1) (3x - 4) = 0
=> x + 1 = 0
x = -1
=> 3x - 4 = 0
x = 4/3
-1 and 4/3 are the zeroes of the given polynomial.
- Verifying the relationship between the zeroes and coefficients :
we know,
Sum of zeroes = -(x coefficient)/x² coefficient
Product of zeroes = constant term/x² coefficient
⇒ Sum of zeroes
= -1 + 4/3
= (-3+4)/3
= 1/3
= -(-1)/3
= -(x coefficient)/x² coefficient
⇒ Product of zeroes
= (-1) (4/3)
= -4/3
= constant term/x² coefficient
Hence verified!
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