Answer:
real and equal
Explanation:
The discriminant of a quadratic equation can provide information about the nature of its roots. Here's what the options mean in this context:
- Real and equal: If the discriminant is positive and equal to zero (in this case, 120), the quadratic equation has real and equal roots. This means that the equation has two identical solutions.
- Complex: If the discriminant is negative, the quadratic equation has complex roots. Complex roots come in pairs of the form a + bi and a - bi, where a and b are real numbers and i is the imaginary unit (√-1).
- Irrational: The concept of irrational roots applies to quadratic equations with coefficients that cannot be expressed as a fraction (e.g., square roots or pi). However, the given discriminant of 120 is positive, so the roots are not irrational.
- Rational: Rational roots are those that can be expressed as a fraction of two integers. However, the given discriminant of 120 is positive, so the roots are not rational.
In this case, since the discriminant is positive (120), the roots of the quadratic equation are real and equal.