Finding zeroes

Question

Find the zeros, if any, of y = 7x2 + 16x + 4 algebraically.

Answer 1

A polynomial takes the form of ax² + bx + c

And to factor a polynomial, we first need to define our constants (a, b, c)

a = 7, b = 16, c = 4

We then multiply a and c which is 7 * 4 = 28

Now we need to find two numbers that add up to equal b and multiply to equal the product of a and c.

So, what two numbers add up to 16 and also when multiplied equal 28?

2 and 14 satisfy both of these requirements.

 

7x² + 16x + 4

= 7x² + 14x + 2x + 4             separate the 16x into our two chosen numbers 2x and 14x

= 7x(x + 2) + 2(x + 2)           factor out common terms

= (7x + 2)(x + 2)                   7x and 2 are both multiplied by (x + 2), we combine like terms--factored

 

Now that we have factored our equation, in order to find the zeroes, or roots, we need to set it equal to zero.

 

(7x + 2)(x + 2) = 0

 

And in order to solve this, we just set each of the sums within the parentheses equal to zero like so:

 

7x + 2 = 0

x + 2 = 0

 

And then solve for x.

Double check by plugging the numbers you find for x into the original equation, and if you get zero, you solved for the correct value of x.

Answer 2

7x² + 16x + 4 = 0            FOIL

(7x + 2)(x + 2) = 0

 

x ∈ {-2/7, -2)