for the follwong equation, state the value of the discriminant and then describe the nature of the solutions:
5^2+9x+2=0
Are you sure you don't mean
5x^2+ 9x+ 2 = 0 ?
The answer to what you wrote is
9x = -27
x = -3
The discriminant is b^2-4ac.
In this case a = 5, b = 9 and c = 2.
Take it from there. You may need to review what the quadratic equation is all about. If so, see
http://en.wikipedia.org/wiki/Discriminant
To find the value of the discriminant for the equation 5x^2 + 9x + 2 = 0 and determine the nature of the solutions, we can utilize the quadratic formula. The quadratic formula states that for an equation in the form ax^2 + bx + c = 0, the solutions are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
By comparing the given equation, 5x^2 + 9x + 2 = 0, with the general form ax^2 + bx + c = 0, we can determine that a = 5, b = 9, and c = 2.
Now, let's calculate the discriminant (denoted as Δ):
Δ = b^2 - 4ac
Substituting the values, we have:
Δ = (9)^2 - 4(5)(2)
Calculating further:
Δ = 81 - 40
Simplifying:
Δ = 41
Therefore, the value of the discriminant is 41.
Next, let's discuss the nature of the solutions based on the discriminant value.
If the discriminant (Δ) is positive, such as in this case, the quadratic equation will have two distinct real solutions. Therefore, the equation 5x^2 + 9x + 2 = 0 has two real solutions.