Question

1. circle all answers that make the inequality true: (x^{2}+3x + 5<9) a. (x = - 1) b. (x = 0) c. (x = 1) d. (x = 2)

Explanation:

Step1: Rearrange the inequality

Subtract 9 from both sides: $x^{2}+3x + 5-9<0$, which simplifies to $x^{2}+3x - 4<0$.

Step2: Factor the quadratic expression

Factor $x^{2}+3x - 4$ as $(x + 4)(x - 1)<0$.

Step3: Find the roots of the corresponding quadratic equation

Set $(x + 4)(x - 1)=0$. The roots are $x=-4$ and $x = 1$. The solution of the inequality $(x + 4)(x - 1)<0$ is $-4

Step4: Check each option

• For $x=-1$, since $-4<-1<1$, it satisfies the inequality.
• For $x = 0$, since $-4<0<1$, it satisfies the inequality.
• For $x = 1$, since $1 = 1$ and the inequality is strict ($<$), it does not satisfy the inequality.
• For $x = 2$, since $2>1$, it does not satisfy the inequality.

Answer:

A. $x=-1$, B. $x = 0$