Question

If alpha and beta are the zeros of the polynomial f(x):- 3*x^2-4*x+1 and find a quadratic polynomial zeros are alpha square/beta and beta square/alpha

Answer 1

hi friend ,

given f(x)=3x²-4x+1

→3x²-3x-x+1

→3x(x-1)-1(x-1)

→(3x-1)(x-1)

so œ,ß are 1/3,1

œ²/ß=1/9---(1)

ß²/œ=3---(2)

given.(1) and (2) are zeros of a polynomial

sum of zeros =1/9+3=28/9

product of zeros =1/3

so polynomial will be

→x²-(28/9)x+1/3

I hope this will help u :)

Answer 2

Hello!

3x²-4x+1

3x²-3x-x+1

3x(x-1)-1(x-1)

(3x-1)(x-1)

x= 1/3 , 1

If α²/β,β²/α are the roots

α²/β=1/9

β²/α=3

x²-(α+β)x+αβ

x²-(3+1/9)x+1/3

x²-28/9x+1/3

9x²-28x+3 is the required polynomial .

hope helped