Question

Write a quadratic equation polynomial whose zeros are 5+√2 & 5-√2

Answer 1

Answer:

if a,b be roots then quadratic equation is

x^2+(sumof roots)x+(product of roots)=0

sum of roots=5+√2+5-√2=5+5=10

product of roots=(5+√2)(5-√2)=25-2=23

equation=x^2-10x+23=0

Answer 2

Answer:

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Answer :

The required quadratic polynomial is

x² - 2√5x + 1

Given :

The zeroes of a quadratic polynomial are :

(√5 + 2) and (√5 - 2)

To Find :

The quadratic polynomial

Formula to be used :

If sum and product of zeroes of a polynomial are given then the polynomial can be written as :

x² - (sum of the zeroes)x + product of the zeroes

Solution :

Given , zeroes :

(√5 + 2) and (√5 - 2)

Sum of the zeroes = √5 +2 + √5 - 2

→ Sum of the zeroes = 2√5

And

product of the zeroes = (√5 + 2)(√5 - 2)

→ product of the zeroes = (√5)² - 2²

→ product of the zeroes =5 - 4

→ product of the zeroes = 1

Therefore , the quadratic polynomial is :

x² - 2√5 x + 1