Question

Find a quadratic polynomial whose zeros are 1 and 3 verify relationships between coefficient and zero of the polynomial

Answer 1

Heya ,,, dear .

Solution is here .......
_____________________________

$let \: \alpha = 1 \: \: and \: \: \beta = 3 \\ \\ sum \: \: of \: zeroes \: ( \alpha + \beta ) = 1 + 3 = 4 \\ \\ product \: \: of \: zeroes \: ( \alpha \beta ) = 1 \times 3 = 3$
$required \: \: polynomial \: \: \\ = {x}^{2} - ( \alpha + \beta )x \: + \alpha \beta \\ = > {x}^{2} - 4x + 3$
We have to verify
_____________

$sum \: of \: the \: \: zeroes \: = 4 = \frac{ - 4}{1} = \frac { - (coefficient \: of \: x)}{coefficient \: of \: {x}^{2} } \\ \\ product \: \: of \: the \: \: zeroes \: = 3 = \frac{3}{1} = \frac{constant \: \: term}{coefficien \: \: of \: {x}^{2} }$
Here, verified
_______________________________

HOPE it's helps you.
☺☺

Answer 2

.........................