Question

-Quadratic Equations-Write a standard form quadratic equation with the given solutions.

Answer 1

Given:

The solution of quadratic equation is,

`w=\frac{-1\pm\sqrt[]{10}}{3}`

So, the roots are written as,

`\begin{gathered} w=\frac{-1+\sqrt[]{10}}{3},\frac{-1-\sqrt[]{10}}{3} \\ (x-(\frac{-1+\sqrt[]{10}}{3}))(x-(\frac{-1-\sqrt[]{10}}{3}))=0 \\ (x+(1)/(3)-\frac{\sqrt[]{10}}{3})(x+(1)/(3)+\frac{\sqrt[]{10}}{3})=0 \\ (x+\frac{1-\sqrt[]{10}}{3})(x+\frac{1+\sqrt[]{10}}{3})=0 \\ x^2+\frac{1+\sqrt[]{10}}{3}x+\frac{1-\sqrt[]{10}}{3}x+(\frac{1-\sqrt[]{10}}{3})(\frac{1+\sqrt[]{10}}{3})=0_{} \\ x^2+(1)/(3)x+\frac{\sqrt[]{10}}{3}x+(1)/(3)x-\frac{\sqrt[]{10}}{3}x+(1-10)/(9)=0 \\ x^2+(2)/(3)x-1=0 \end{gathered}`

Answer: The standard form quadratic equation is,

`x^2+(2)/(3)x-1=0`