Question

f and g are the zeroes of ax²+bx+c then find f³+g³ ​

Answer 1

Answer:

given quadratic equation = ax² + bx + c

sum of zeros = -b/a

=> f + g = -b/a

and

product of zeroes = c/a

=> fg = c/a

$now \\ {f}^{3} + {g}^{3} = ( {f + g)}^{3} - 3fg(f + g) \\ = { (\frac{ - b}{a}) }^{3} - 3 \frac{c}{a} ( \frac{ - b}{a} ) \\ = \frac{ { - b}^{3} }{ {a}^{3} } + \frac{3bc}{ {a}^{2} } \\ = \frac{ - {b}^{3 } + 3abc}{ {a}^{3} } \\ = \frac{3abc - {b}^{3} }{ {a}^{3} } .$