Question

What polynomial has roots of -6, -4, and 1

x^3 - 9x^2 -22x +24
x^3 -x^2 -26x -24
x^3 +x^2 -26x +24
x^3 +9x +14x -24

Answer 1

put in the polynomial x=1 ,x=-4,x=-6 for that polynomial for for which you get zero is the root.
for example put x=1 in x^3 - 9x^2 -22x +24
(1)^3-9(1)^2-22(1)+24=-6 since i am not getting zero so x=1 is not a root.
try the same for the above all polynomials.

Answer 2

(x+6)*(x+4)*(x-1)=0 - this equation can be formed from the given roots.
Simplify it to get the answer x^3 +9x^2 +14x -24 = 0

Answer 3

@sami-21 's method also works well but takes a little bit more time.

Answer 4

sum of roots = -b/a
sum of product in pair = c/a
and product = -d/a
find these coefficients and hence you have the eqn..
for simplicity, take a=1 ..

Answer 5

just by checking for -b/a ,,you have your ans straightaway,,
hope am explaining this clear enough,,