zeroesof the polynomialfind a quadratic polynomial whezĂŠroes areaor

1.	zeroesof the polynomialfind a quadratic polynomial whezĂŠroes areaor
Answer» Alphaand β are the zeros of 3x²-4x +1 polynomial, first of all we factorise 3x²-4x+13x² -4x + 1 =3x² -3x -x +1 =3x( x -1) -1(x -1) =(3x -1)(x -1) hence. (3x -1) and (x -1) are the factors of given polynomial . so, x = 1/3 and 1 are the zeros of that polynomial. hence, α = 1/3. and β = 1or α = 1 and β. = 1/3you can choose any one in both I choose α = 1. and β = 1/3 now,let any unknown. polynomial. whose zeros are α²/β and β²/α α²/β = (1)²/(1/3) = 3 β²/α = (1/3)²/1 = 1/9 now, equation of unknown polynomial. x²- ( sum of roots)x + product of roots = x²- ( α²/β + β²/α)x +(α²/β)(β²/α) put α²/β = 3 and β²/α = 1/9 = x²- ( 3 +1/9)x + 3 × 1/9 = x² -28x/9 + 3/9 ={ 9x² -28x + 3 }1/9 hence, 9x² -28x + 3 is answer

Answer»

Alphaand β are the zeros of 3x²-4x +1 polynomial,

first of all we factorise 3x²-4x+13x² -4x + 1

=3x² -3x -x +1

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

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

hence. (3x -1) and (x -1) are the factors of given polynomial .

so, x = 1/3 and 1 are the zeros of that polynomial.

hence, α = 1/3. and β = 1or α = 1 and β. = 1/3you can choose any one in both

I choose α = 1. and β = 1/3

now,let any unknown. polynomial. whose zeros are α²/β and β²/α

α²/β = (1)²/(1/3) = 3

β²/α = (1/3)²/1 = 1/9

now, equation of unknown polynomial.

x²- ( sum of roots)x + product of roots

= x²- ( α²/β + β²/α)x +(α²/β)(β²/α)

put α²/β = 3 and β²/α = 1/9

= x²- ( 3 +1/9)x + 3 × 1/9

= x² -28x/9 + 3/9

={ 9x² -28x + 3 }1/9

hence, 9x² -28x + 3 is answer

Discussion