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  • Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. x ^2 -2x - 8

Q1 (1)   Find the zeroes of the following quadratic polynomials and verify the relationship between
              the zeroes and the coefficients.  x ^2 - 2x -8

Answers (1)

best_answer

x2 - 2x - 8 = 0

x2 - 4x + 2x - 8 = 0

x(x-4) +2(x-4) = 0

(x+2)(x-4) = 0

The zeroes of the given quadratic polynomial are -2 and 4

\\\alpha =-2\\ \beta =4

VERIFICATION

Sum of roots:

\\\alpha+\beta =-2+4=2

\\-\frac{coefficient\ of\ x}{coefficient\ of\ x^{2}}\\ =-\frac{-2}{1}\\ =2\\=\alpha +\beta

Verified

Product of roots:

\\\alpha \beta =-2\times 4=-8

\\\frac{constant\ term}{coefficient\ of\ x^{2}}\\ =\frac{-8}{1}\\ =-8\\=\alpha \beta

Verified

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Sayak

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