Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient.
$6 x^{2} - 3 - 7 x$

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Solution

$6 x^{2} - 7 x - 3 = 0$

$\Rightarrow 6 x^{2} + 2 x - 9 x - 3 = 0$

$\Rightarrow 2 x (3 x + 1) - 3 (3 x + 1) = 0$

$\Rightarrow (2 x - 3) (3 x + 1) = 0$

$\Rightarrow \frac{3}{2}, \frac{- 1}{3}$ are zeroes
Sum of zeroes $= \frac{3}{2} - \frac{1}{3} = \frac{9 - 2}{6} = \frac{7}{6} = \frac{- (- 7)}{6}$

Product of zeroes $= \frac{4}{2} \times \frac{- 1}{3} = \frac{- 1}{2} = \frac{- 3}{6}$

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6 x^{2} - 3 - 7 x

Question 1 (iii)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

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

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