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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:

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

4x^2 - 3x - 1

Answers (1)

Answer. \left [1, -\frac{1}{4} \right ]

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

4x^2 - 3x - 1

4x^2 - 4x + x - 1

4x(x - 1) + 1(x - 1)

(x -1) (4x + 1)

x – 1 = 0                                  4x + 1 = 0

x = 1                                        4x = –1

                                             x=-\frac{1}{4}               

Hence, 1, -\frac{1}{4}  are the zeroes of the polynomials

4x^2 - 3x - 1

a = 4, b = -3, c = -1

We know that

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

Here, 1 + \left (\frac{-1}{4} \right )=\frac{4-1}{4}=\frac{3}{4}

Which is equal to -\frac{b}{a}

Product of zeroes \frac{c}{a}=\frac{-1}{4}

Here 1 \times \frac{-1}{4}=\frac{-1}{4}=\frac{c}{a}

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