How do you use the discriminant to determine the nature of the solutions given # y = x^2 – 7x + 7#?
Have a look if it is not too confusing...!
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.