Question

Given the standard form of a quadratic equation y=ax²+bx+c with 2 real and unique roots, what can be said about the discriminant?

Answer 1

The discriminant of a quadratic equation with 2 real and unique roots will be positive.

Step-by-step explanation:

The discriminant of a quadratic equation in standard form, y = ax² + bx + c, can be used to determine the nature of the roots. If the discriminant, D = b² - 4ac, is positive, then the equation has two real and unique roots. If the discriminant is zero, then the equation has two real and identical roots. If the discriminant is negative, then the equation has no real roots.

For example, if we have the equation y = 2x² + 5x + 2, we can calculate the discriminant as follows: D = 5² - 4(2)(2) = 9. Since the discriminant is positive, the equation has two real and unique roots.

Therefore, if a quadratic equation in standard form has two real and unique roots, we can say that the discriminant will be positive.