Which statement about the following equation is true?

[tex]2 x^2-9 x+2=-1[/tex]

A. The discriminant is less than 0, so there are two real roots.
B. The discriminant is less than 0, so there are two complex roots.
C. The discriminant is greater than 0, so there are two real roots.
D. The discriminant is greater than 0, so there are two complex roots.

The discriminant for the equation 2 x 2 − 9 x + 2 = − 1 is calculated to be 57, which is greater than 0. This indicates that there are two distinct real roots for the equation. Therefore, the correct option is C: The discriminant is greater than 0, so there are two real roots.
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Answered by Anonymous | 2025-07-03

To determine which statement about the equation 2 x 2 − 9 x + 2 = − 1 is true, we first need to set it to zero by moving all terms to one side:
2 x 2 − 9 x + 2 + 1 = 0
This simplifies to:
2 x 2 − 9 x + 3 = 0
Next, we calculate the discriminant of this quadratic equation. The discriminant D is calculated using the formula:
D = b 2 − 4 a c
For our equation, a = 2 , b = − 9 , and c = 3 . Substituting these values in, we get:
D = ( − 9 ) 2 − 4 × 2 × 3
Calculate each part:

( − 9 ) 2 = 81
4 × 2 × 3 = 24

So the discriminant is:
D = 81 − 24 = 57
Since the discriminant D = 57 is greater than 0, it indicates that there are two distinct real roots for the quadratic equation.
Therefore, the correct statement is:
C. The discriminant is greater than 0, so there are two real roots.

Answered by OliviaLunaGracy | 2025-07-06