107
Find the zeroes of the polynomial $p(x) = 3x^2 - 2x - 1$ and verify the relationship between the zeroes of $p(x)$ and the coefficients of $p(x)$.
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Solution:
$p(x) = 3x^2 - 2x - 1$
$= (3x + 1)(x - 1)$
Zeroes are $x = -\frac{1}{3}, 1$ [1 mark]
$\text{Sum of zeroes} = -\frac{1}{3} + 1 = \frac{2}{3} = \frac{-\text{coefficient of } x}{\text{coefficient of } x^2}$ [1 mark]
$\text{Product of zeroes} = -\frac{1}{3} \times 1 = \frac{-1}{3} = \frac{\text{constant term}}{\text{coefficient of } x^2}$ [1 mark]
$p(x) = 3x^2 - 2x - 1$
$= (3x + 1)(x - 1)$
Zeroes are $x = -\frac{1}{3}, 1$ [1 mark]
$\text{Sum of zeroes} = -\frac{1}{3} + 1 = \frac{2}{3} = \frac{-\text{coefficient of } x}{\text{coefficient of } x^2}$ [1 mark]
$\text{Product of zeroes} = -\frac{1}{3} \times 1 = \frac{-1}{3} = \frac{\text{constant term}}{\text{coefficient of } x^2}$ [1 mark]