We call it discriminating the radical B2-4ac which is represented by the Greek letter (delta).
We can now write in this way Bhaskara's formula:
According to the discriminant, we have three cases to consider:
1st case: the discriminant is positive .
The value of is real and the equation has two different real roots, represented as follows:
For which values of k the equation x² - 2x + k- 2 = Does it admit real and unequal roots?
SolutionFor the equation to admit real and unequal roots, we must have
Therefore, the values of k must be less than 3.
2nd case: the discriminant is null
The value of is null and the equation has two real and equal roots, represented as follows:
Determine the value of P, so that the equation x² - (P - 1) x + p-2 = 0 has equal roots.
Solution:For the equation to admit equal roots, it is necessary that .
Therefore, the value of P é 3.
3rd case: the discriminant is negative .
The value of doesn't exist in GOtherefore there are no real roots. The roots of the equation are complex number.
For what values of m does equation 3x² + 6x +m = 0 admit no real root?
Solution:In order for the equation to have no real root, we must have
Therefore, the values of m must be greater than 3.
Given the equation ax² + bx + c = 0, we have:
For , the equation has two different real roots.