Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients

3x^{2} – x – 4

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#### Solution

3x^{2} – x – 4 = 3x^{2} – 4x + 3x – 4

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

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

The zeroes of the polynomial are {4/3, -1}

Relationship between the zeroes and the coefficient of the polynomial:

Also sum of the zeroes = ` 4/3 -1 = (4 - 3)/3 = 1/3`

Also product of the zeroes = `4/3x -1 = - 4/3`

Hence verified

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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