Question

find the zeroes of the quadratic polynomial 3x2 -75 and verify the relationship between zeroes and coefficients

Answer 1

$3x ^{2} - 75 = 0$

$3(x ^{2} - 25) = 0$

$3((x) ^{2} - (5) ^{2} ) = 0$

$3(x + 5)(x - 5) = 0$

$(x + 5)(x - 5) = 0$

$either$

$x + 5 = 0$

$x = - 5$

$or$

$x -5 = 0$

$x = 5$

$verification$

$sum \: \: of \: \: zeroes \: \: = \frac{ - b}{a}$

$5 + ( - 5) = \frac{0}{3}$

$0 = 0$

$product \: \: of \: \: zeroes = \frac{c}{a}$

$5 \times ( - 5) = \frac{ - 75}{3}$

$- 25 = - 25$

Answer 2

3x ^{2}  - 75 = 0

3(x ^{2}  - 25) = 0

3((x) ^{2}  - (5) ^{2} ) = 0

3(x + 5)(x  - 5) = 0

(x + 5)(x - 5) = 0

either

x + 5 = 0

x =  - 5

or

x -5  = 0

x = 5

verification

sum \:  \: of \:  \: zeroes \:  \:  =  \frac{ - b}{a}  

5 + ( - 5) =  \frac{0}{3}  

0 = 0  

product \:  \: of \:  \: zeroes =  \frac{c}{a}  

5 \times ( - 5) =  \frac{ - 75}{3}  

 - 25 =  - 25