Question

What are the roots of the equation 4x2 – 100 = 0?a. -25 and 25b. -25 onlyc. -5 and 5d. -5 onlyNeed to show work!!

Answer 1

Consider the given equation,

`4x^2-100=0`

Add 100 both sides,

`\begin{gathered} 4x^2-100+100=0+100 \\ 4x^2=100 \end{gathered}`

Divide by 4 both sides,

`\begin{gathered} 4x^2\cdot(1)/(4)=100\cdot(1)/(4) \\ x^2=25 \end{gathered}`

Take square roots both sides,

`\begin{gathered} x=\pm\sqrt[]{25} \\ x=-5,5 \end{gathered}`

Thus, the roots of the given equation are -5 and 5.

Therefore, option C is the correct choice.