Question

find the quadratic polynomial , the sum and product of whose zeroes are √3 and 1/√3 . verify the relationship between the zeros and coefficients of polynomial ​

Answer 1

Answer:

I think this is your Answer !

Let the zeroes of the quadratic polynomial be α=1,β=−3

Then, α+β=1+(−3)=−2

αβ=1×(−3)=−3

Sum of zeroes =α+β=−2

Product of zeroes =αβ=−3

Then, the quadratic polynomial =x2−( sum of zeroes )x+ product of zeroes =x2−(−2)x+(−3)=x2+2x−3

Verification:

Sum of zeroes =α+β=1+(−3)=−2 or 

=− Coefficient of x2 Coefficient of x=−1(2)=−2

Product of zeroes =αβ=(1)(−3)=−3 or 

= Coefficient of x2 Constant term =1−3=−3

So, the relationship between the zeroes and the coefficients is verified.

Answer 2

Answer:

sum = root3 , so - b/a = root3 - (i) product = 1/root 3 , so c/a =1/root3 - (ii)

On comparing 1. and 2. , a = root3 , b = (-3) and c = 1 , so p(x) = root3x square - 3x + 1