Question

What is the nature of roots of 2x² 6x 3 0?

Answer 1

The roots are imaginary.

Explanation:

⭐ What is "the nature of the roots"

• The nature of the roots are how the roots of a quadratic exist.

⭐What are the different types of "the nature of the roots"?

• The roots could be real numbers, distinct, and rational/irrational
• The roots could be real, equal, and rational
• The roots could be imaginary

⭐How do we determine "the nature of the roots"?

• Substitute the values of the coefficients (a,b, and c) of a quadratic equation into the quadratic formula(
  `x =( -b+/-√(b^2-4ac) )/(2a)`)
• If the value of the discriminant in the quadratic formula (
  `b2-4ac`)>0: the roots are real numbers, distinct, and rational/irrational
• If the value of the discriminant in the quadratic formula (
  `b2-4ac`)=0: the roots are real, equal, and rational
• If the value of the discriminant in the quadratic formula (
  `b2-4ac`)<0: the roots are imaginary

To solve this problem, substitute the values of the coefficients of the given quadratic equation into the quadratic formula:

`x =( -6+/-√(6^2-4(2)(30)) )/(2(2))`

Now, compute only the discriminant (
`b^2-4ac`).

`b^2-4ac = 36-4(60)`

`b^2-4ac = 36-240`

`b^2-4ac = -204`

`b^2-4ac`< 0. Therefore, the roots are imaginary.