ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2aSince the given equation is already in standard form, we can identify the values of a, b, and c.
2x^2-6x+9=0 ⇔ 2x^2+( - 6)x+ 9=0
Now, let's evaluate the discriminant.
b We want to use the discriminant of the given quadratic equation to determine the number and type of the roots. If we do not want to know the exact values of the roots, we only need to work with the discriminant. From Part A, we know that the discriminant of the given equation is - 36.
Equation:& 2x^2-6x+9=0
Discriminant:& - 36
Since the discriminant is less than zero, the quadratic equation has two complex roots.
Extra
Further information
If the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions.
