Question

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$6 straight x squared minus 3 minus 7 straight x$

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Solution

We have,6x²–7x–3 = 6x²– 9x + 2x – 3
= 3x(2x – 3) + 1(2x – 3)
= (3x + 1) (2x – 3)
So, the value of 6x² – 7 – 3 is zero when (3a + 1) = 0 or (2x – 3) = 0
i.e.

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Now,
Sum of zeroes =

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space space space equals fraction numerator negative left parenthesis Coefficient space of space straight x right parenthesis over denominator Coefficient space of space straight x squared end fraction

Product of zeroes =

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fraction numerator Constant space term over denominator Coefficient space of space straight x squared end fraction.

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Polynomials

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
$6 straight x squared minus 3 minus 7 straight x$

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