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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: t^3 – 2t^2 – 15t

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

t^3 - 2t^2 - 15t

Answers (1)

Answer. [0, 5, -3]

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

t^3 - 2t^2 - 15t =0        (a = 1, b = –2, c = –15, d = 0)

t(t^2 - 2t - 15) =0

t(t^2 - 5t + 3t - 15)=0

t(t(t - 5) + 3(t - 5))=0

t(t - 5) (t + 3)=0

t = 0                 t – 5 = 0                       t + 3 = 0

                        t = 5                             t = –3

Hence, 0, 5, –3 are the zeroes of the polynomial

Sum of zeroes =\frac{-b}{a}=\frac{-(-2)}{1}=2

Here, 0 + 5 - 3 = 2 = \frac{-b}{a}

Product of zeroes = \frac{-d}{a} = \frac{0}{1} = 0.

Here, 0 \times 5\times 3 = 0 = \frac{-d}{a}

If \alpha ,\beta ,\gamma are three roots the\alpha \beta +\beta \gamma +\gamma \alpha =\frac{c}{a}

(0 \times 5) + (5 \times - 3) + (-3 \times 0) = -\frac{15}{1}

-15 = -15

Hence proved.

Posted by

infoexpert21

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