Question

Which shows the un-simplified solution for x2 + 8x + 6 = 0?

Answer 1

Choice A

Explanation:

Let's solve to check.

Given:

x^2 + 8x + 6 = 0

Solution:

We know that,

• Let us assume that Quadratic Formula = x

`\implies \rm \: x = \cfrac{ { - b±} \sqrt{ {b}^(2) - 4(ac)} }{2a}`

• Here, a = 1
• b = 8
• c =6

So substitute them:

`\implies \rm \: x = \cfrac{ - 8± \sqrt{ {8}^(2) - 4(1 * 6)} }{2 * 1}`

`\implies \rm \: x = \cfrac{ - 8± √(64 - 4 * 6 ) }{2}`

`\implies \rm \: x= \cfrac{ - 8 ±√(64 - 24) }{2}`

`\boxed{ \implies \rm \: x = \cfrac{ - 8 ±√(40)}{2}}`

Hence, choice A[x = {8±√(40)/2}] shows the un-simplified solution for x2 + 8x + 6 = 0.

Answer 2

A)
`\displaystyle x=(-8\pm√(40))/(2)`

Explanation:

We know that the discriminant is
`b^2-4ac=(8)^2-4(1)(6)=64-24=40`, so it cannot be B or C.

Also, because
`2a=2(1)=2`, then the denominator must be 2, which means that A is the correct un-simplified solution for the quadratic equation.