Question

Solve the quadratic equation by using the quadratic formula. If the solutions are not real, enter NA. 3x2−5x+1=0 Enter the exact answers.

Answer 1

The given quadratic equation is,

`3x^2-5x+1=0`

let us use the formula,

`\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where,

`\begin{gathered} a=3 \\ b=-5 \\ c=1 \end{gathered}`

subistute the values in the formula,

`\begin{gathered} =\frac{-(-5)\pm\sqrt[]{(-5)^2-4*3*1}}{2*3} \\ =\frac{5\pm\sqrt[]{25-12}}{6} \\ =\frac{5\pm\sqrt[]{13}}{6} \\ x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6} \end{gathered}`

The roots of the quadratic equation are ,

`x=\frac{5+\sqrt[]{13}}{6},x=\frac{5-\sqrt[]{13}}{6}`