Question

What are the values of x that satisfy the equation x2 + 4x - 1 = 0?

O A-
45
O B 4+13
OC -2 13
D. 2+5

Answer 1

Step1: write out the equation

`x^2+4x-1=0^{}`

Looking at the equation it cannot be factorized, hence we use the quadratic formula method

Step2: write out the quadratic formula

`\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ \end{gathered}`

where a=coefficient ofx²=1

b=coefficient of x=+4

c= constant =-1

Step3: Substitute the values into the formula above

`x=\frac{-4\pm\sqrt[]{4^2-4(1)(-1)}}{2(1)}`
`\begin{gathered} x=\frac{-4\pm\sqrt[]{16+4}}{2} \\ =\frac{-4\pm\sqrt[]{20}}{2} \end{gathered}`

Hence, by splitting the denominator we have

`\begin{gathered} x=(-4)/(2)\pm\frac{\sqrt[]{20}}{2} \\ =-2\pm\frac{\sqrt[]{4*5}}{2} \\ =-2\pm\frac{2\sqrt[]{5}}{2} \\ =-2\pm\sqrt[]{5} \end{gathered}`

x=-2±√5

Therefore the right option is c