Question

the two roots alpha and beta of a quadratic equation are related by the equations alpha+beta=9,alpha-beta=1. Form an equation whose roots are 3alpha and beta.​

Answer 1

Answer:

x^2 - 19x + 60

Step-by-step explanation:

α + β = 9     &  α - β = 1

Add both, 2α = 10 ⇒ α = 5

Hence, β = 9 - 5 = 4

 So, if we form an equation with roots 3α and β,

sum of roots = 3α + β

     = 3(5) + 4 = 19

product of roots = (3α)(β)

            = 3(5)(4)  = 60

In a quadratic equation, x^2 - Sx + P,  sum of roots is S  and product of roots is P.

Hence the required equation is,

x^2 - Sx + P

x^2 - (19)x + (60)

x^2 - 19x + 60

Answer 2

Step-by-step explanation:

I hope you don't is clear