Question

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

Answer 1

Answer:

The roots are imaginary.

Step-by-step 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( $x =\frac{ -b+/-\sqrt{b^2-4ac} }{2a}$)
• 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:

$x =\frac{ -6+/-\sqrt{6^2-4(2)(30)} }{2(2)}$

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.