Question

Find quadratic polynomial whose zeroes are : 3+√7,3-√7

Answer 1

Let the quadratic polynomial be ax²+ bx + c, and its zeroes be α and β.

We have

Sum of zeroes =(α+ β)=3+√7+3-√7=6=-b/a

Product of zeroes= (α β)=(3+√7)(3-√7)=3²-(√7)²

=9-7=2= c/a

If a=1, b=-6 and c=2

So, one quadratic polynomial which fits the given conditions is x²-6x+2