Question

If alpha, beta are zeroes of (2x2) - (4x) + 5 find value of (square root of alpha over beta) + (square root of beta over alpha)

Answer 1

Answer:

2√2 / √5

Step-by-step explanation:

Given polynomial : 2x² - 4x + 5

α, β are the zeroes

Comparing with ax² + bx + c we get,

• a = 2
• b = - 4
• c = 5

Sum of zeroes = α + β = - b / a = - ( - 4 ) / 2 = 2

Product of zeroes = αβ = c / a = 5 / 2

√( α / β ) + √( β / α )

= √α / √β + √β / √α

= [ ( √α )² + (√β)² ] √αβ

= ( α + β ) / √αβ

= 2 / √( 5 / 2 )

= 2 / ( √5 / √2 )

= 2√2 / √5

Therefore the value of √( α / β ) + √( β / α ) is 2√2 / √5.