Question

If alpha and beta are zeroes of quadratic polynomial f(x)=3x^2-5x-2,then evaluate

i) alpha^2+beta^2 ii) alpha^3+beta^3

Answer 1

Question :

If α and ß are zeroes of quadratic polynomial f(x)=3x²-5x-2,then evaluate

(I) α² + ß²

(ii) α³ + ß³



Answer :

(I) α² + ß² = 37/9

(ii) α³ + ß³ = 215/8


Step - By - Step Explanation :


Given Equation : f(x) = 3x²-5x-2

•°• Sum of Zeroes = -b/a

Sum of Zeroes ( α + ß ) = 5/3

•°• Product of Zeroes = c/a

Product of Zeroes ( α.ß ) = -2/3


To Find :

(I) α² + ß²

= (α + ß )² - 2αß

= ( 5/3 ) ² - 2 × -2/3

= (25/9) + 4/3

= 25 + 12 / 9

= 37 / 9


( ii ) α³ + ß³

= ( α + ß ) ( α² - αß + ß² )

= ( α + ß ) [ ( α² + ß² - αß) ]

= ( α + ß ) [ ( α + ß)² - 2αß - αß ]

= ( 5/3 ) [ ( 5/3)² - 3× -2/3

= ( 5/3) [ ( 25/9 + 2 ) ]

= ( 5/3) [ ( 25 +18 /9 ) ]

= ( 5/3) [ ( 43/9 ) ]

= ( 5/3 × 43/9 )

= 215 / 18