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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: 5t^2 + 12t + 7

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

5t^2 + 12t + 7

Answers (1)

Answer.        \left [-1, -\frac{7}{5} \right ]

Zeroes : zeroes of the polynomial are the values(s) the makes it equal to 0

5t^2 + 12t + 7

5t^2 + 5t + 7t + 7

5t(t + 1) + 7(t + 1)

(t + 1) (5t + 7)

t + 1 = 0                       5t + 7 = 0

t = –1               t =\frac{-7}{5}

Hence, \left [-1, -\frac{7}{5} \right ]are the zeroes of polynomial

Sum of zeroes \frac{-b}{a}=\frac{-12 }{5}

Here, -1-\frac{7}{5}=\frac{-5-7}{5}=\frac{-12}{5}=\frac{-b}{a}

Product of zeroes \frac{c}{a}=\frac{7}{5}

Here, -1 \times -\frac{7}{5}=\frac{7}{5}=\frac{c}{a}

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