Question

find the quadratic polynomial whose one zero is (2 +√5) and the other is (2 - √5)​

Answer 1

Answer:

x²-4x-1

Step-by-step explanation:

Given:- (2+√5) and (2-√5) are the zeroes of required quadratic polynomial

Now, Sum Of zeroes=(2+√5)+(2-√5)

= 2 +√5+2-√5

= 2+2=4

Product of zeroes=(2+√5)(2-√5)

{using a²-b²=(a+b)(a-b)}

= 2²-√5²

=4-5

= -1

f(x)=x²-(Sum Of zeroes)x+Product of zeroes

=x²-4x-1

Therefore, the reqd. polynomial is x²-4x-1

I hope it helps you