Question

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answer 1

C

Explanation:

We want to solve the equation:

`x^2+2x+7=0`

Using the quadratic formula. The quadratic formula is given by:

`\displaystyle x=(-b\pm√(b^2-4ac))/(2a)`

In this case, a = 1, b = 2, and c = 7.

Substitute:

`\displaystyle x=(-(2)\pm√((2)^2-4(1)(7)))/(2(1))`

Evaluate:

`\displaystyle x=(-2\pm√(-24))/(2)`

Simplify the square root:

`√(-24)=√(4\cdot 6\cdot -1)=√(4)\cdot√(6)\cdot√(-1)=2i√(6)`

Hence:

`\displaystyle x=(-2\pm2i√(6))/(2)`

Simplify:

`\displaystyle x=-1\pm i√(6)`

Hence, our solutions are:

`\displaystyle x=\left\{-1+i√(6), -1-i√(6)\right\}`

Our answer is C.