Answer:
Option C
Step-by-step explanation:
The complete question is in the attachment.
The given equation is
[tex]2 {x}^{2} - 9x + 2 = - 1[/tex]
We rewrite in standard form to get;
[tex]2 {x}^{2} - 9x + 3 = 0[/tex]
Compare to
[tex]a {x}^{2} + bx + c = 0[/tex]
we have a=2, b=-9 and c=3.
We substitute into the formula for the discriminant:
[tex]D= {b}^{2} - 4ac[/tex]
We substitute to get:
[tex]D= {( - 9)}^{2} - 4 \times 2 \times 3[/tex]
[tex]D=81- 24 = 57[/tex]
Since the discriminant is greater than zero, there are two real roots.
