Find the sum and product of the zeroes polynomial $6 x^{2} - 4 - 5 x$ [2 MARKS]

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Solution

Zeros : 1 Mark
Sum of zeros : 0.5 Mark
Product of zeros : 0.5 Mark

Given polynomial is,

$6 x^{2} - 4 - 5 x$

$= 6 x^{2} - 5 x - 4$ [Arranging them in the standard form]

$= 6 x^{2} - 8 x + 3 x - 4$

$= 2 x (3 x - 4) + 1 (3 x - 4)$

$= (2 x + 1) (3 x - 4)$

For the zeroes,

$2 x + 1 = 0 \Rightarrow x = - \frac{1}{2}$

$3 x - 4 = 0 \Rightarrow x = \frac{4}{3}$

Their sum and product is,

$α + β = - \frac{1}{2} + \frac{4}{3} = \frac{5}{6}$

$α β = - \frac{1}{2} \times \frac{4}{3} = - \frac{2}{3}$

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