The quantity b² - 4ac of a given quadratic equation is called its discriminant. The quadratic equation will have 2 rational roots.
How to use the discriminant to find the property of solutions of a given quadratic equation?
Let the quadratic equation given be of the form ax² + bx + c = 0, then
The quantity b² - 4ac is called it's discriminant.
The solution contains the term √[b² - 4ac] which will be:
- Real and distinct if the discriminant is positive
- Real and equal if the discriminant is 0
- Non-real and distinct roots if the discriminant is negative
There are two roots of quadratic equations always(assuming the existence of complex numbers). We say that the considered quadratic equation has 2 solutions if roots are distinct, and has 1 solution when both roots are the same.
Given the discriminant of a quadratic equation is 28, which is positive or greater than zero, therefore, the quadratic equation will have 2 rational roots.
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