3.2 Show that $$ k $$ lie $$ k^{2}+7 k \leq 8 $$

Question

UpStudy AI · Accepted Answer

Solve the equation $$ k^{2}+7k-8=0 $$.
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
  $$k^{2}+7k-8=0$$
- step1: Factor the expression:
  $$\left(k-1ight)\left(k+8ight)=0$$
- step2: Separate into possible cases:
  $$\begin{align}&k-1=0\&k+8=0\end{align}$$
- step3: Solve the equation:
  $$\begin{align}&k=1\&k=-8\end{align}$$
- step4: Rewrite:
  $$k_{1}=-8,k_{2}=1$$
The solutions to the equation $$k^{2}+7k-8=0$$ are $$k=-8$$ and $$k=1$$.

Therefore, the inequality $$k^{2}+7k \leq 8$$ is satisfied when $$k$$ lies between -8 and 1.
The inequality $$k^{2}+7k \leq 8$$ holds true when $$k$$ is between -8 and 1.

3.2 Show that lie

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions