Question

If a, b and c are the roots of the equation x

Answer 1

Question: If a, b, and c are the roots of the equation $x³-4x²+3x+5$, what is the value of (a+1)(b+1)(c+1)?

Answer:

for cubic equations, $ax³+bx²+cx+d$, with roots a,b and c

$a+b+c = -b/a\\ ab+bc+ac = c/a\\ abc = -d/a$

$(a+1)(b+1)(c+1) = (a+b+c) + (ab+bc+ac) + abc + 1 = 4 + 3 -5 + 1 = 3$