Find the sum and product of the zeroes polynomial $9 x^{2} - 6 x + 1$ . [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,

$9 x^{2} - 6 x + 1$

$= 9 x^{2} - 3 x - 3 x + 1$

$= 3 x (3 x - 1) - 1 (3 x - 1)$

$= (3 x - 1)^{2}$

For the zeroes,

$(3 x - 1)^{2} = 0 \Rightarrow x = \frac{1}{3}$

Their sum and product is,

$α + β = \frac{1}{3} + \frac{1}{3} = \frac{2}{3}$

$α β = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

$A l t e r n a t i v e m e t h o d :$
$S u m o f z e r o s = α + β = \frac{- b}{a} = \frac{- (- 6)}{9} = \frac{2}{3}$ ,
$P r o d u c t o f z e r o s = \frac{c}{a} = \frac{1}{9}$ .

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