SOLUTION: If a quadratic equation has the discriminant of 16, what is NOT true about its solutions? All solutions are rational numbers All solutions are real numbers All solutions are i

Question 1031995: If a quadratic equation has the discriminant of 16, what is NOT true about its solutions?
All solutions are rational numbers
All solutions are real numbers
All solutions are integers
There are two solutions
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The discriminant is positive, so "All solutions are real numbers" and "There are two solutions" are true.

The solutions do not have to be integers (take for example,

which has discriminant 16, but whose solutions are -5/6 and 1/2). Moreover, the solutions do not necessarily have to be rational - given an equation

, let a = 1, b =

, and c be the number such that

. Since

is irrational, the solutions are irrational.

For quadratic equations in one variable with real coefficients and discriminant 16, the statements "All solutions are integers" and "All solutions are rational" do not have to be true.
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