Question

HEY GUYS...SOLVE THIS ONE

Find the quadratic polynomial whose zeros are 2 and (-6) respectively.Verify the relation between coefficients and the zeros of the polynomial.​

Answer 1

Hi..

zeroes are 2 and -6

▪sum of zeroes =(S)= 2+(-6) => -4
▪product of zeroes =(P) = 2×(-6) => -12

▪so polynomial = x^2 - Sx + P

x^2 +4x -12

□verification:-

▪$sum = \frac{ - b}{a}$

$= \frac{ - 4}{1}$

$= - 4$

▪$product = \frac{c}{a}$

$\frac{ - 12}{1}$

$= - 12$

hence verified..

#tq

Answer 2

❗❗ʜᴏʟᴀ!! ❗❗

ʜᴇʀᴇ ɪs ʏᴏᴜʀ ᴀɴsᴡᴇʀ!! ⬇⬇⬇⬇

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ʜᴇʀᴇ 2 ᴀɴᴅ -6 ᴀʀᴇ ᴛʜᴇ ʀᴏᴏᴛs ᴏғ ᴛʜᴇ 
ᴘᴏʟʏɴᴏᴍɪᴀʟ. ⭐

ᴀs ᴡᴇ ᴋɴᴏᴡ ᴛʜᴀᴛ, ⭐

ᴘᴏʟʏɴᴏᴍɪᴀʟ =

${x}^{2} - (sum \: of \: the \: roots)x \\ + its \: product$

So,

Sum = 2 + (-6) = 2 - 6 = -4✔

And

Product = 2 * (-6) = -12✔

$so \: polynomial =$

${x}^{2} - ( - 4)x \: + ( - 12)$

↪Therefore......

${x}^{2} + 4x - 12$

This is the Answer.. ✔

Verification :-

Sum of Zeroes
= -b/a
= -4/1
= -4

Product of Zeroes
= c/a
= -12/1
=- 12

Hence verified.. __✔

✨Hope my answer is helpful!! ✨

Thanks!!! ✌