Question

Determine the number of real solutions to each quadratic equation 4u^2 - 20u + 25=0

Answer 1

Step-by-step explanation

We are to determine the number of real solutions to the quadratic equation

`4u^2-20u+25=0`

To do this we will make use of the quadratic formula:

`\begin{gathered} u_(1,\:2)=(-\left(-20\right)\pm √(\left(-20\right)^2-4\cdot \:4\cdot \:25))/(2\cdot \:4) \\ \\ \\ u_(1,\:2)=(-\left(-20\right)\pm √(0))/(2\cdot \:4) \\ \\ u_(1,2)=(-\left(-20\right)\pm0)/(2*\:4) \\ \\ u_1=(20+0)/(8)=(20)/(8)=(5)/(2)=2.5 \\ u_2=(20-0)/(8)=(20)/(8)=(5)/(2)=2.5 \\ \end{gathered}`

Therefore, we can see that it has one real solution which is 2.5