Question

Find the quadratic polynomial whose zeroes are
2+√3 and 2-√3​

Answer 1

x^2 -4x +1=0 will be the answer


We know the relationship between zeros and coefficients of polynomial
i.e , if the equation ax^2+bx+c=0 is having 2 roots p and q then p.q =c/a
And p+q = -b/a ,

Here let p=2+ √3
and q= 2-√3

Now p.q = (2+ √3 )(2-√3 ) =1
Which is equal to c/a

Now p+q = 2+ √3 +2- √3 =4
Which is equal to -b/a

Now if you compare the equations -b/a=4 , and c/a=1

With quadratic equation ax^2 + bx +c =0

We know that equation can also be written in the form : x^2 -(p+q)x + (p.q)

You will get the equation as x^2 -4x +1 , which you have to find