It’s allowed to replace any of three coefficients of quadratic trinomial by its discriminant. Is it true that from any quadratic trinomial that does not have real roots, we can perform such operation several times to get a quadratic trinomial that have real roots?
If the quadratic ax^2+bx+c is considered, the discriminant is D=b^2-4ac. For the quadratic to have no real roots, the discriminant must be negative. A necessary but not sufficient requirement for negative D is that a and c must be the same sign (both positive or both negative).
For the case of a and c both positive, if either one is replaced by D, which is negative, then the resulting new discriminant becomes positive, and the new quadratic will then have real roots.
Still working on the case where a and c are both negative
|
|
Posted by Kenny M
on 2021-04-25 07:03:48 |
Partial Solution