Question

find the Discriminant and describe the number and type of solutions of the equations.1) 4x2 + 8x + 4 =0

Answer 1

We are given the following quadratic equation

`4x^2+8x+4=0`

The standard form of a quadratic equation is given by

`ax^2+bx+c=0`

Comparing the given equation with the standard form, the coefficients are

a = 4

b = 8

c = 4

The discriminant is given by

`D=b^2-4ac`

Let us substitute the values of coefficients

`\begin{gathered} D=8^2-4(4)(4) \\ D=64-64 \\ D=0 \end{gathered}`

So what does it mean?

D > 0 means there are 2 real solutions

D = 0 means there is 1 real solution

D < 0 means there is no real solution (imaginary solutions)

Since D = 0, therefore, the given equation has 1 real solution.