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Answered

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[tex] {3x}^{2} + 6x + 1 = 0[/tex]
[tex] {3x}^{2} + 6x + 1 = 0[/tex]

a, Are the roots equal or unequal? b. Are the roots rational or irrational? C. Are the roots real or non-real?​

Sagot :

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Answer:

  • the roots are unequal (distinct)
  • the roots are irrational
  • the roots are real

Step-by-step explanation:

A description of the roots of a quadratic can be had by looking at the value of the discriminant: b²-4ac, where a, b, c are the coefficients of the standard-form quadratic.

Here, we have a=3, b=6, c=1 so the discriminant is ...

  d = 6² -4(3)(1) = 24

This is a positive integer that is not a perfect square. This value means ...

  • the roots are unequal (distinct)
  • the roots are irrational
  • the roots are real

_____

The interpretation of the discriminant is ...

  • d > 0, distinct real roots
  • d = 0, one real root with multiplicity 2
  • d < 0, complex roots

If d is an integer that is not a perfect square, the roots (or their imaginary part) will be irrational.

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