Question

Compute the value of the discriminant and give the number of real solutions of the quadratic equation.-4x²+2x–5=0

Answer 1

`\begin{gathered} \text{Discriminant}=-76 \\ No\text{ real solutions} \end{gathered}`

Step-by-step explanation

We want to find the discrimininant of the equation:

`-4x^2+2x-5=0`

The general form of a quadratic equaion is given as:

`ax^2+bx+c=0`

The discriminant is given as:

`b^2-4ac`

Therefore, we need to find that.

From the given equation:

`\begin{gathered} a=-4 \\ b=2 \\ c=-5 \end{gathered}`

Therefore, we have that the discriminant is:

`\begin{gathered} 2^2-4(-4)(-5) \\ 4-(4\cdot20) \\ 4-80 \\ -76 \end{gathered}`

That is the discriminant.

Since the discriminant is less than 0, then there are no real solutions of the equation.