Question

if alpha and beta are two zeroes of 2x^2-4x+6, find a quadratic polynomial whose zeroes are alpha/beta^2 and beta/alpha^2

Answer 1

Answer:

Step-by-step explanation:

Kindly see this and mark brainliest

Answer 2

The required quadratic equation is 9x²+10x+3.

Given,

α and β are the zeroes of the polynomial 2x²-4x+6.

To Find,

The quadratic polynomial whose roots are α/β² and β/α².

Solution,

α and β are the zeroes of the polynomial 2x²-4x+6, So

α+β = 4/2 = 2

αβ = 6/2 = 3

Now, the value of

α/β²+β/α² = (α³+β³)/(αβ)²

α/β²+β/α = ((α+β)³-3αβ(α+β))/(3²)

α/β²+β/α = (2³-3*3(2))/9 = -10/9

Now,

α/β²*β/α² = 1/αβ = 1/3

Now, the required quadratic equation will be

x²-(α/β²+β/α²)x+α/β²*β/α²

Now, substituting the values

x²+10/3x+1/9

9x²+10x+3

Hence, the required quadratic equation is 9x²+10x+3.

#SPJ3