Question

Determine the discriminant, and then state the nature of the solutions. x^2+4x+7=0The discriminant tells us there is Answer

Answer 1

The discriminant of a quadratic equation is given by:

`\begin{gathered} b^2-4ac \\ \text{with the quadratic equation in the form} \\ ax^2+bx+c=0 \end{gathered}`

•When the calculation of the discriminant gives a negative number, the equation has two complex roots

•when the discriminant is zero, the equation has a root, double root

•when the calculation of the discriminant is a positive number, the equation has two distinct roots.

the given quadratic equation is

`\begin{gathered} x^2+4x+7=0 \\ \text{In this equation, the coefficients will tell us that values for }a,b,\text{ and }c \\ a=1 \\ b=4 \\ c=7 \end{gathered}`

Substitute these values to get the discriminant.

`\begin{gathered} b^2-4ac \\ =(4)^2-4(1)(7) \\ =16-28 \\ =-12 \end{gathered}`

Since the discriminant is negative, we can conclude that there is two complex solutions.