Question

if alpha and beta be two zeros of quadratic polynomial x2-7x+12. find a quadratic polynomial whose zeros are -alpha and -beta ​

Answer 1

Step-by-step explanation:

In a quadratic equation, ax^2 + bx + c,   sum S of roots is given by - b/a   and product P of roots is c/a.

In this equation,  

S = α + β = -(-7/1) = 7

P = αβ = 12/1 = 12

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

sum of roots = -α + (-β)

        = - α - β  = - (α + β)  

        = - 7

product of roots = (-α)(-β)

               = (αβ)

               = 12

Hence the required equation is,

⇒ x^2 - (-7)x + 12

⇒ x^2 + 7x + 12