If α & β are the zeros of the quadratic polynomial f(x)=3x 2 – 4x + 1, find a quadratic polynomial whose zeros are alfa square/beta and beta square /alfa
Answers
Answer:
Step-by-step explanation:
Given that,
α and β are the zeroes of the polynomial f ( x ) = 3x² - 4x + 1 .
Comparing the given equation with ax² + bx + c = 0,
We have a = 3 , b = - 4 and c = 1.
∴ x = - b ±√b² - 4ac /2a
= - ( - 4 ) ± √( - 4 )² - 4 ( 3 ) ( 1 ) / 2 ( 3 )
= 4 ± √ 16 - 12 / 6
= 4 ± √4 / 6
= 4 ± 2/6
= 4 ± 1/3
= 4 + 1/3 or 4 - 1/3
= 12 + 1 / 3 or 12 - 1 / 3
= 13/3 or 11/3.
∴ α = 13/3 and β = 11/3.
∴ α² / β + β² / α = [ ( 13/3)² / (11/3) ] + [ (11/3)² / ( 13/3 ) ]
= ( 169/9 × 3/11 ) + ( 121/ 9 × 3/13 )
= ( 169 / 33 ) + ( 121 / 39 )
= ( 169 × 13 + 11 × 121 / 429 )
= ( 2197 + 1331 / 429 )
= 3528 / 429 is the answer.