48.1k views
0 votes
F(x)=x^2+2x-8 Can you use the factoring method or the Quadratic formula to arrive at the roots?

User Myslik
by
7.6k points

1 Answer

3 votes

Answer:

To determine if we can use factoring or the Quadratic formula to find the roots of the function F(x) = x^2 + 2x - 8, we need to check if the function is factorable or if it fits the criteria for the Quadratic formula.

Let's start by checking if the function can be factored. For a quadratic function to be factorable, the coefficient of the x^2 term should be 1, and the constant term should be a product of two numbers that add up to the coefficient of the x term.

In our function, the coefficient of the x^2 term is 1, which is good. However, the constant term, -8, cannot be factored into two numbers that add up to 2, the coefficient of the x term. Therefore, we cannot use factoring to find the roots of this function.

Now, let's move on to the Quadratic formula. The Quadratic formula is a useful tool for finding the roots of any quadratic function of the form ax^2 + bx + c = 0, where a, b, and c are constants.

The Quadratic formula is given by: x = (-b ± √(b^2 - 4ac))/(2a)

For our function F(x) = x^2 + 2x - 8, the coefficients are:

a = 1 (coefficient of x^2 term)

b = 2 (coefficient of x term)

c = -8 (constant term)

Now, we can plug these values into the Quadratic formula and solve for x. Let's do that:

x = (-2 ± √(2^2 - 4(1)(-8)))/(2(1))

Simplifying further:

x = (-2 ± √(4 + 32))/2

x = (-2 ± √36)/2

x = (-2 ± 6)/2

Now, we can simplify the equation further by separating it into two solutions:

x1 = (-2 + 6)/2 = 4/2 = 2

x2 = (-2 - 6)/2 = -8/2 = -4

Therefore, the roots of the function F(x) = x^2 + 2x - 8 are x = 2 and x = -4.

User Tristan Beaton
by
7.6k points

No related questions found