Question

if alpha +beta =8 and alpha square + beta square =34,find the quadratic equation whose roots are alpha and beta?​

Answer 1

Therefore the equation is x^2-8x+15=0

Answer 2

The quadratic equation whose roots are alpha and beta is x² - 8x + 15 = 0 .

Given in the question α + β = 8 and α² + β² = 34

α = 8 - β

Put value of α in α² + β² = 34 to get the value of α and β

=> (8 - β)² + β² = 34

=> 2β² - 16β + 64 = 34

=> β² - 8β +15 = 0

=> β = 5 , 3

when β = 5 , the value of α = 3

when β = 3 , the value of α = 5

The Sum of roots = α + β = 8

The product of roots = α × β = 15

The quatratic equation having roots as α and β -

x² - (sum of roots) x + product of roots = 0

=> x² - (α + β)x + αβ = 0

=> x² - 8x + 15 = 0