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  • Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials: 3x^2 + 4x – 4

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:

3x^2 + 4x - 4

Answers (1)

Answer.        \left [-2, \frac{2}{3} \right ]

Solution. Zeroes : zeroes of the polynomial are the value(s) that makes it equal to 0.

3x^2 + 4x - 4

3x^2 + 6x - 2x -4

3x(x + 2) - 2(x + 2)

(x + 2) (3x - 2)

x + 2 = 0               3x - 2 = 0

x = -2                   x =\frac{2}{3}

Hence, \left [-2, \frac{2}{3} \right ]  are the zeroes of the polynomial

3x^2 + 4x - 4

a = 3, b = 4, c = –4

Sum of the zeroes =-\frac{b}{a}=-\frac{4}{3}

Here, -2+\frac{2}{3}=\frac{-6+2}{3}=\frac{-4}{3}=\frac{-b}{a}

Product of the zeroes \frac{c}{a}=\frac{-4}{3}

Here, -2 \times \frac{2}{3}=\frac{-4}{3}=\frac{c}{a}

 

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