Question

if 4and 1are the sum and product of a quadractic polynomial then the polynomial is​

Answer 1

Let α and β are zeros of required quadratic polynomial.

⇒  α+β=4                 ---- ( 1 )        [ given ]

⇒  αβ=1               ----- ( 2 )          [ Given ]

The required polynomial,

x2−(α+β)x+(αβ)=0

Now, using ( 1 ) and ( 2 )

⇒  x2−4x+1=0         

Answer 2

Let alpha and beta are required quadratic polynomial

alpha + beta = 4 ----(1) [given]

alpha• beta = 1 ----(2) [given]

The required polynomial,

x²–(alpha+beta)x + (alpha•beta) = 0

Now, using 1 and 2,

━≫ x²–4x+1=0