Question

Cubic Equation :-
x³+0x²+6x-3=0 has roots alpha, beta and gamma.
Find value of:-
alpha cube + beta cube +gamma cube

Answer 1

alpha beta + beta gamma + gana Alpha equals to c/a
= -3/1
= -3
p(X)= x cube + 0 x square + 6 x minus 3 equals to 0
p p(-3)= (-3) cube + 0 (-3) square + 6 (-3) minus 3 equals to 0
= -27+0-18
= -27-18
= x=-45

Answer 2

Final Answer : 9
Let the roots of cubic equation be a, b, c.

We know that,
a+b+c = 0
ab+bc+ac= 6
abc= 3

Now,
$( {a}^{3} + {b}^{3} + {c}^{3} ) = \\ (a + b + c)( {a}^{2} + {b}^{2} + {c}^{2} - ab - bc - ac) \\ + 3abc = > \\ 0 \times ( \: \: \: \: ) + 3 \times 3 \\ = > 9$

Final Answer is 9