Question

write an equation for a polynomial that has the solution set {-1, 3, 4}.
\bigcirc (x + 1)(x + 3)(x + 4) = 0
\bigcirc (x - 1)(x + 3)(x + 4) = 0
\bigcirc (x + 1)(x - 3)(x - 4) = 0
\bigcirc (x - 1)(x + 3)(x - 4) = 0

#7 *

if the roots of a quadratic equation are -2 and 3, the equation can be written as
a. (x - 2)(x + 3) = 0 \t\t b. (x + 2)(x - 3) = 0

Explanation:

Step1: Relate roots to factors

If $r$ is a root, $(x-r)$ is a factor.
For roots $-1, 3, 4$:
Factors are $(x-(-1))=(x+1)$, $(x-3)$, $(x-4)$
Equation: $(x+1)(x-3)(x-4)=0$

Step2: Relate roots to quadratic factors

For roots $-2, 3$:
Factors are $(x-(-2))=(x+2)$, $(x-3)$
Equation: $(x+2)(x-3)=0$

Answer:

1. $(x + 1)(x - 3)(x - 4) = 0$
2. B. $(x + 2)(x - 3) = 0$