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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. 3x ^2 - x - 4

Q1 (6)   Find the zeroes of the following quadratic polynomials and verify the relationship between
             the zeroes and the coefficients. 3 x^2 - x - 4

Answers (1)
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S Sayak

3x2 - x - 4 = 0

3x2 + 3x - 4x - 4 = 0

3x(x + 1) - 4(x + 1) = 0

(3x - 4)(x + 1) = 0

The zeroes of the given quadratic polynomial are 4/3 and -1

\\\alpha =\frac{4}{3}\\ \beta =-1

VERIFICATION

Sum of roots:

\\\alpha +\beta =\frac{4}{3}+(-1)=\frac{1}{3}

\\-\frac{coefficient\ of\ x}{coefficient\ of\ x^{2}}\\ =-\frac{-1}{3}\\ =\frac{1}{3}\\=\alpha +\beta

Verified

Product of roots:

\alpha \beta =\frac{4}{3}\times -1=-\frac{4}{3}

\\\frac{constant\ term}{coefficient\ of\ x^{2}}\\ =\frac{-4}{3}\\ =\alpha \beta

Verified

  

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