Keyword Analysis & Research: real rational and unequal

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Are the roots of a rational function real and unequal?

So the roots are real and unequal. We cannot say if the roots are rational or irrational since this depends on the exact value of \(k\).

What is the difference between unequal and irrational?

Unequal means that the discrimanent can't equal zero b/c + or -0 will get you roots that are equal. Irrational means that it is a fraction. This means the discriminant cannot be a perfect square.

When are the roots of a quadratic equation irrational and unequal?

When a, b, and c are real numbers, a ≠ 0 and the discriminant is positive but not a perfect square then the roots of the quadratic equation ax 2 + bx + c = 0 are real, irrational and unequal. Here the roots α and β form a pair of irrational conjugates. Case VI: b 2 – 4ac > 0 is perfect square and a or b is irrational

How do you know if a discriminant is rational or irrational?

If the discriminant is positive and is a perfect square (ex. 36,121,100,625 ), the roots are rational. If the discriminant is positive and is not a perfect square (ex. 84,52,700 ), the roots are irrational. A positive discriminant has two real roots (these real roots can be irrational or rational).