For the following equation, state the value of the discriminant and then describe the nature of the solutions.
-2x^2+3x-7=0
What is the value of the discriminant?
Which one of the statements below is correct?
The equation has two imaginary solutions.
The equation has one real solution.
The equation has two real solutions.
first of all, I always have my quadratic equations start with a positive coefficient of the square term, so...
2x^2 - 3x + 7 = 0
disc.= 9 - 4(2)(7) = -47
Depending of the value of this discriminant, your text book should have the basic and most fundamental information about the nature of the roots.
Let us know what you have decided as to the 3 choices.
I would choose a - the equation has two imaginary soluations. Is this right?
correct
If the disc. is negative, you would have two complex roots.
Thank you.
4x² + 3x - 1
To find the value of the discriminant, we need to use the formula:
Discriminant (D) = b^2 - 4ac
In the given equation -2x^2+3x-7=0, we can identify the values of a, b, and c:
a = -2
b = 3
c = -7
Substituting these values into the formula, we have:
D = (3)^2 - 4(-2)(-7)
D = 9 - 56
D = -47
Therefore, the value of the discriminant is -47.
Now, let's analyze the nature of the solutions based on the value of the discriminant.
If the discriminant is greater than 0 (D > 0), then the equation has two real solutions.
If the discriminant is equal to 0 (D = 0), then the equation has one real solution.
If the discriminant is less than 0 (D < 0), then the equation has two imaginary solutions.
Since the value of the discriminant is -47, which is less than 0 (D < 0), we can conclude that the correct statement is:
The equation has two imaginary solutions.