Question

If alpha and bita are the two zeros of the quadratic polynomial x^2-3x+7 find a quadratic polynomial whose zeroes are 1/alpha and 1/bita

Answer 1

ʜᴇy ʙʀᴏ
__________________________________________________________________________________________
x²-3x+7
$\alpha + \beta = - ( \frac{b}{a} )$
$\alpha + \beta = - ( \frac{ - 3}{1} )$

$\alpha + \beta = 3$
$\alpha \beta = \frac{c}{a}$
$\alpha \beta = \frac{7}{1}$
$\alpha \beta = 7$
ʟᴇᴛ ꜱ ᴀɴᴅ ᴩ ʙᴇ ᴛʜᴇ ꜱᴜᴍ ᴏꜰ ᴀɴᴅ ᴩʀᴏᴅᴜᴄᴛ ᴏꜰ ᴢᴇʀᴏꜱ...
$s = \frac{1}{ \alpha } + \frac{1}{ \beta }$
$= \frac{ \alpha + \beta }{ \alpha \beta }$
$= \frac{3}{7}$

$p = \frac{1}{ \alpha } \times \frac{1}{ \beta }$
$= \frac{1}{ \alpha \beta }$
$= \frac{1}{7}$
ʟᴇᴛ ᴛʜᴇ ʀᴇqᴜɪʀᴇᴅ ᴩᴏʟyɴᴏᴍɪᴀʟ ɪꜱ x²-ꜱx+ᴩ
ɪᴇ=x²-3/7x+1/7
=7x²-3x+1
______________________________________________________________________
ʜᴏᴩᴇ ɪᴛ ʜᴇʟᴩꜱ

Answer 2

$\orange{\boxed{\blue{\boxed{\green{Hope \: It \: May \: Help \: You}}}}}$