standard form with -5and 1/2 as it’s roots

Answer 1

Hi Camila!

I'm assuming you're working with quadratic equations/polynomials in this problem. :)

First, what is the standard form of a quadratic equation? Looking up the definition, we see:

y = ax² + bx + c

This will be what our final answer looks like.

Okay, now, how can we use the roots to find the answer? Well, let me explain the idea using a different/easier example. Usually, when we solve a quadratic equation like y = x² + 5x + 6 we factor it and set it equal to 0. Like this:

x² + 5x + 6 = 0

(x + 2)(x + 3) = 0

We then set each equal to 0:

x + 2 = 0 and x + 3 = 0

And solving gives us the roots:

x = -2 and x = -3.

Great, but how does that help us? Well, we can start with the roots the question gave us and work backwards to get the equation! Like this.... we know the roots are:

x = -5 and x = 1/2

So, they must have come from:

x + 5 = 0 and x - 1/2 = 0

These must have come from:

(x + 5)(x - 1/2) = 0

Since those are the factors, we can multiply it out to get the equation:

(x + 5)(x - 1/2) = x² + 5x - 1/2 x - 5/2 = x² + 9/2 x - 5/2

The answer is y = x² + 9/2 x - 5/2.

Hope that helps! Let me know if you have any questions on the steps!