Question

6x + 1 = 0" alt=" {3x}^{2} + 6x + 1 = 0" align="absmiddle" class="latex-formula">
${3x}^{2} + 6x + 1 = 0$

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

Answer 1

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.