Answer:
9) we get value of x: [tex]\mathbf{x=-4+\sqrt{42}\:i, x=-4-\sqrt{42}\:i}[/tex]
Option C is correct.
10) The difference is [tex]2k^3+3k-1[/tex]
Option A is correct.
Step-by-step explanation:
9) We need to solve:
[tex]x^2+8x+58=0[/tex]
Solving using quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a=1, b=8 and c=58
Putting values and finding value of x
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-8\pm\sqrt{(8)^2-4(1)(58)}}{2(1)}\\x=\frac{-8\pm\sqrt{64-232}}{2}\\x=\frac{-8\pm\sqrt{-168}}{2}\\We\:know\sqrt{-1}=i \\x=\frac{-8\pm2\sqrt{42}\:i}{2}\\x=\frac{2(-4\pm\sqrt{42}\:i)}{2}\\x=\frac{2(-4+\sqrt{42}\:i)}{2}, x=\frac{2(-4-\sqrt{42}\:i)}{2}\\x=-4+\sqrt{42}\:i, x=-4-\sqrt{42}\:i[/tex]
So, we get value of x: [tex]\mathbf{x=-4+\sqrt{42}\:i, x=-4-\sqrt{42}\:i}[/tex]
Option C is correct.
10) [tex](5-2k^3-5k)-(-4k^2+6-8k)[/tex]
Combining like terms and subtracting:
[tex](5-2k^3-5k)-(-4k^3+6-8k)\\=5-2k^3-5k+4k^3-6+8k\\=-2k^3+4k^3-5k+8k+5-6\\=2k^3+3k-1[/tex]
The difference is [tex]2k^3+3k-1[/tex]
Option A is correct.
