Question

Determine the number of real solutions to each quadratic equation Homework question. Not a test or exam

Answer 1

Given

Quadratic Equation

`r^2+18r+81=0`

Find

Number of real solutions

Step-by-step explanation

The value of discriminant tells us the nature of solutions of a given equation.

if D>0 , then the equation has two distinct real roots.

if D=0, then the equation has two equal real roots.

if D<0, then the equation has two conjugated complex roots.

so,

`r^2+18r+81=0`

discriminant =

`\begin{gathered} D=b^2-4ac \\ D=(18)^2-4*1*81 \\ D=324-324 \\ D=0 \end{gathered}`

here D =0 , then it has two equal real solution.

Final Answer

Hence , it has two equal real solutions