Question

find the quadratic equation if one of the root is√5- √3​

Answer 1

Answer:

let f(x)=ax^2+bx+c=0 is qe

and x=√5-√3

factor of f(x) will be

X-√5+√3

now qe=(x+(√3-v5))^2

= x^2+2(√3-√5)x+2(1-√15)

Answer 2

Answer:

if one root is given then second root will be -(√5-√3)

therefore, roots are a = √5-√3 and b= -(√5-√3)

put these in General quadratic equation which is

x^2 -(a+b) x +ab=0

a+b = 0

ab = -(8-2√15)

so equation is

x^2 - 0- (8-2√15) =0

x^2 = 8 - 2√15 ans

I hope this is correct.