Question

(a) If a and ß be two zeros of the quadratic polynomial
ax2 + bx + c, then evaluate
(1) 1/a³​

Answer 1

Answer:

The polynomial is ax² + bx + c whose zeroes are α and β.

The sum of the zeroes = α+β = -b/a

The product of the zeroes = α.β = c/a

Therefore,

1/ a³ + b³

=> 1/ (a+b)³ - 3ab(a+b)

=> 1/ (-b/a)³ - 3c/a(-b/a)

=> 1/ -b³/a³+3bc/a²

=> 1/ -b³+3bc/a³

=> - a³/b³ + 3bc.