# How do you determine if a solution to a quadratic equation is rational or irrational by using the discriminant?

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To determine if a solution to a quadratic equation is rational or irrational using the discriminant, you can follow these steps:

- Write the quadratic equation in the standard form: ( ax^2 + bx + c = 0 ).
- Identify the coefficients ( a ), ( b ), and ( c ) in the equation.
- Calculate the discriminant using the formula: ( \Delta = b^2 - 4ac ).
- If the discriminant ( \Delta ) is greater than zero (( \Delta > 0 )), then the quadratic equation has two distinct real roots, which are rational numbers.
- If the discriminant ( \Delta ) is equal to zero (( \Delta = 0 )), then the quadratic equation has one real root, which is a rational number (repeated root).
- If the discriminant ( \Delta ) is less than zero (( \Delta < 0 )), then the quadratic equation has two complex roots, which are irrational.

That's how you can determine if a solution to a quadratic equation is rational or irrational using the discriminant.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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