Question

quadratic functions, equations, and relations assessment lep checkpoint complete the following problems. show all your work. learning goal from lesson 3.1 i can define i. i can describe complex numbers in terms of their real and imaginary parts. how i did (circle one) i got it! im still learning it. a radical expression is shown below. what is the simplified form of this expression? (1/2 point) 1. √(-150) what are the solutions for the given equations below? (1/2 point each) 2. 2x² - 7 = 1 3. 3n² - 27 = 0 4. w² + 9 = 3

Explanation:

Step1: Simplify $\sqrt{-150}$

Rewrite as $\sqrt{-1\times150}=\sqrt{-1}\times\sqrt{150}$. Since $\sqrt{-1}=i$, and $\sqrt{150}=\sqrt{25\times6} = 5\sqrt{6}$, so $\sqrt{-150}=5i\sqrt{6}$.

Step2: Solve $2x^{2}-7 = 1$

First, add 7 to both sides: $2x^{2}=1 + 7=8$. Then divide both sides by 2: $x^{2}=4$. Take square - roots of both sides, $x=\pm\sqrt{4}=\pm2$.

Step3: Solve $3n^{2}-27 = 0$

Add 27 to both sides: $3n^{2}=27$. Divide both sides by 3: $n^{2}=9$. Take square - roots of both sides, $n=\pm\sqrt{9}=\pm3$.

Step4: Solve $w^{2}+9 = 3$

Subtract 9 from both sides: $w^{2}=3 - 9=-6$. Take square - roots of both sides, $w=\pm\sqrt{-6}=\pm i\sqrt{6}$.

Answer:

1. $5i\sqrt{6}$
2. $x = 2,x=-2$
3. $n = 3,n=-3$
4. $w = i\sqrt{6},w=-i\sqrt{6}$