Sum

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

6x^{2} – 3 – 7x

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#### Solution

6x^{2} - 3 - 7x = 6x^{2} - 7x - 3

=6x^{2} -9x + 2x -3

=3x(2x - 3) + 1(2x - 3)

=(2x - 3)(3x + 1)

=`2(x - 3/2)3(x+1/3)`

=`6(x - 3/2)(x+1/3)`

The zeroes of the polynomial are `{3/2, -1/3}`

Relationship between the zeroes and the coeffieicients of the polynomial

Also sum of the zeroes = `3/2 - 1/3=(9-2)/6 = 7/6`

Also product of the zeroes =`3/2 xx -1/3= -1/2`

Hence Verified

Concept: Relationship Between Zeroes and Coefficients of a Polynomial

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