Question

If alpha and beta be the zeroes of the quadratic polynomial 3x^2×5x×7 evaluate 1/Alpha cube+1/beta cube

Answer 1

Step-by-step explanation:

alpha + beta = -5/3

alpha×beta = 7/3

I'm assuming the "×" in your question is "+".

For simplicity, a denotes alpha, b denotes beta.

1/a cube + 1/b cube

= (a cube + b cube)/(a×b cube)

= (a + b)((a + b) square - 3ab)/(a×b cube)

= (-5/3)((-5/3)^2 - 3 × 7/3)/(7/3)^3

= (-5/3)((25-63)/9)/(49×7)/27

= (5 × 38)/(49 × 7)

= 190/343