Question

If (α) and (β) are the Zeroes of the quadratic polynomial f(x) = 3x² − 4x + 1 , Find a quadratic polynomial , whose Zeroes are α²/β and β²/α .

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Answer 1

Step-by-step explanation:

we have

3x^2 - 4x + 1 = 0

alpha + beta = 4 /3 Alpha .Beta = 1 /3

alpha ^2 / beta ^2 + beta^2 / alpha^2

= ( alpha + beta ) ( a^2 + b^2 - ab)/ab

= ( a+ b ) [( a+b)^2 - 3ab] / 1/3

= 4 ( 16/9 - 1 ) = 4×7 /9 = 28/9

= a^2 / B × b^2 / a = aB = 1/3

Hence ,

quadratic equation whose roots are a^2 / B and B^2 / a

= x ^2 + 28/9x + 1/3 = 0

9x^2 - 28 + 3= 0

Hope it helps you

Answer 2

Step-by-step explanation:

P(x)=3x^2-4x+1,

by splitting the middle term,

3x^2-3x-x+1=0,

3x(x-1)-1(x-1)=0,,

(3x-1)(x-1)=0,

3x-1=0, or, x-1=0,

x=1/3, or, x=1,

or the zeros of the quadratic polynomial p(x)= 3x^2-4x+1 are 1/3 and 1,

let the new polynomial be f(x) having zeroes as ,

(1/3)^2/1 and 1^2/1/3,

1/9 and 3,

f(x)=x^2-( sum of zeroes)x+ product of zeroes,

=x^2-(1/9+3)x+1/9×3,

=x^2-28/9x+3/9,

=9x^2-28x+3