For the quadratic equation x squared plus 3 x plus 5 equals 0, find the value of the discriminant to determine if the equation has a real or non-real solution.
For quadraic equation:
a x² + b x +c
∆ = b² - 4 a c
is the discriminant
The discriminant is used to determine the number of solutions in the quadratic equation.
There are three cases:
If ∆ < 0 the equation has two conjugate complex solutions
If ∆ = 0 the equation has one real solution
If ∆ > 0 the equation has two non-real (conjugate complex solutions)
In this case:
x² + 3 x + 5
The coefficients are:
a = 1 , b = 3 , c = 5
∆ = b² - 4 a c = 3² - 4 ∙ 1 ∙ 5 = 9 - 20 = - 11
∆ < 0
So the equation x² + 3 x + 5 has two non-real (conjugate complex solutions).
My typo.
If ∆ < 0 the equation has two non-real (conjugate complex solutions)
If ∆ = 0 the equation has one real solution
If ∆ > 0 the equation has two real solutions
Oh, discriminants can be so dramatic! Okay, let's calculate it: for the quadratic equation x^2 + 3x + 5 = 0, the discriminant (denoted by Δ) is given by the formula Δ = b^2 - 4ac. Here, a = 1, b = 3, and c = 5. So, plugging those values in, we have Δ = (3)^2 - 4(1)(5). Are you ready for the big reveal? *drumroll* After the calculations, we find that Δ = -11. Negative discriminant, huh? That means the equation has non-real solutions. Guess the solutions will be partying in the realm of complex numbers! 🎉🎩
To find the value of the discriminant, you can use the formula:
Discriminant = b^2 - 4ac
For the given quadratic equation, x^2 + 3x + 5 = 0, we can identify the values as follows:
a = 1 (coefficient of x^2)
b = 3 (coefficient of x)
c = 5 (constant term)
Now, substitute these values into the discriminant formula:
Discriminant = (3)^2 - 4(1)(5)
= 9 - 20
= -11
Therefore, the discriminant is -11. Since the discriminant is negative, the quadratic equation has non-real (complex) solutions.
To find the discriminant of a quadratic equation, you can use the formula:
Discriminant (D) = b^2 - 4ac
In the equation, x^2 + 3x + 5 = 0, the coefficients are as follows:
a = 1 (the coefficient of x^2)
b = 3 (the coefficient of x)
c = 5 (the constant term)
Substituting these values into the formula, we can calculate the discriminant:
D = (3)^2 - 4 * 1 * 5
= 9 - 20
= -11
The discriminant of this quadratic equation is -11.
Since the discriminant is negative (-11 < 0), the equation does not have any real solutions. Instead, it has two non-real (complex) solutions.