Question

form the quadratic equation whose roots are 4+√5 and 4-√5​

Answer 1

Answer:

x² - 8x + 11 = 0

Step-by-step explanation:

Let,

α = 4 + √5

β = 4 - √5

α + β = 4 + √5 + 4 - √5

= 4 + 4 + √5 - √5

α + β = 8

αβ = ( 4 + √5 ) ( 4 - √5 )

= ( 4 )² - ( √5 )²

= 16 - 5

αβ = 11

x² - ( α + β )x + αβ = 0

x² - 8x + 11 = 0

Therefore, the quadratic equation is x² - 8x + 11.