Question

Which of the following quadratic equations has the solutions2+1322X2Required: Choose an answer!A. 3x2 + 4x + 1 = 0OB. 4x2 – 8x + 1 = 0C. x2 + 3x + 2 = 0D. x2 - 4x + 3 = 0PrevNext

Answer 1

Given the solution of the equation:

`x=\frac{2\pm\sqrt[]{3}}{2}`

Let's check which quadratic equations has the given solution,

`\begin{gathered} A)3x^2+4x-1=0 \\ \text{compare with ax}^2+bx+c=0 \\ a=3,b=4,c=-1 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-4\sqrt[]{4^2+12}}{2\cdot3} \\ =(-4\pm\:2√(7))/(2\cdot\:3) \\ x_{}=(-2+√(7))/(3),\: (-2-√(7))/(3) \end{gathered}`
`\begin{gathered} B)4x^2-8x+1=0 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=(-\left(-8\right)\pm√(\left(-8\right)^2-4\cdot\:4\cdot\:1))/(2\cdot\:4) \\ x=(-\left(-8\right)\pm\:4√(3))/(2\cdot\:4) \\ x=(2\pm√(3))/(2) \end{gathered}`

Hence, the correct option is B) 4x²-8x+1=0