Find the zeroes of the following equations and the sum and product of the zeroes

1) $6 x^{2} - 4 - 5 x$

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

3) $4 x^{2} - x - 3$

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Solution

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

= $(2 x + 1) (3 x - 4)$ , the zeroes are $- \frac{1}{2} & \frac{4}{3}$ ;

their sum and product is $\frac{5}{6}$ & $- \frac{2}{3}$

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

= $(3 x - 1)^{2}$ , the zeroes are $\frac{1}{3} & \frac{1}{3}$ ;

sum is $\frac{2}{3}$ (also = $- \frac{b}{a}$

product is $\frac{1}{9}$ (also = $\frac{c}{a}$ )

$4 x^{2} - x - 3$ factorized is

= $(4 x + 3) (x - 1)$ , the zeroes are $1, - \frac{3}{4}$

sum is $\frac{1}{4}$

product is $- \frac{3}{4}$

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