Question

Evaluating a quadratic ex Evaluate the expression when x x^(2)+6x+8

Answer 1

The value of the quadratic expression
`x^2` + 6x + 8 when x = -2 is 0.

Step-by-step explanation:

The given quadratic expression is
`x^2` + 6x + 8. To evaluate this expression for a specific value of x, in this case, x = -2, we substitute -2 for x in the expression:

`\[(-2)^2 + 6(-2) + 8\]`

Simplifying this expression step by step:

`\[= 4 - 12 + 8\]`

`\[= 0\]`

Therefore, when x = -2, the value of the quadratic expression
`x^2` + 6x + 8 is 0. This means that (-2) is a root of the quadratic equation, making the expression equal to zero.

In the quadratic expression,
`x^2` + 6x + 8, we can also determine its factors by factoring:

`\[x^2 + 6x + 8 = (x + 2)(x + 4)\]`

Setting each factor equal to zero and solving for x gives the roots of the quadratic equation. In this case, when (x + 2) = 0, x = -2, and when (x + 4) = 0, x = -4.

So, the quadratic expression has roots at x = -2 and x = -4. Substituting x = -2 into the expression verifies that it indeed evaluates to 0, confirming the root of the quadratic equation at x = -2