Complete Question:
Which statement about the following equation is true?
[tex]2x^2-9x+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
Answer:
C) The discriminant is greater than 0, so there are two real roots
Step-by-step explanation:
The given equation is [tex]2x^2-9x+2 = -1[/tex] which by simplification becomes
[tex]2x^2 - 9x + 3 = 0[/tex]
For a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex], the discriminant is given by the equation, [tex]D = b^2 - 4ac[/tex]
If the discriminant D is greater than 0, the roots are real and different
If the discriminant D is equal to 0, the roots are real and equal
If the discriminant D is less than 0, the roots are imaginary
For the quadratic equation under consideration, a = 2, b = -9, c = 3
Let us calculate the discriminant D
D = (-9)² - 4(2)(3)
D = 81 - 24
D = 57
Since the Discriminant D is greater than 0, the roots are real and different.
