# How do you use the discriminant to determine the nature of the solutions given # y = x^2 – 7x + 7#?

##### 1 Answer

Have a look if it is not too confusing...!

#### Explanation:

The discriminant, or Delta

In your case you have a function, that tells you all the possible solutions (combinations of

For example, if you choose

One interesting case is when:

But...no problem we use the discriminant to figure out what kind of solutions we'll get.

We consider the general form of our equation:

where the corresponding numerical coefficients, in our equation, are:

and the formula for the discriminant:

and we get:

Our Delta is bigger than zero so this implies that our equation will be satisfied by 2 real and distinct values of

If Delta was equal to zero we'd had 2 real coincident values (basically two equal numbers).

A value of Delta less than zero would imply no real solutions available for our equation.