Question

Which two values of x are roots of the polynomial below?4x2 - 6x + 1D AX=-8 - 1286-6I B. X =€ + √5216O c. x=6- V20X8O D. =-6 - 5216D E.-8 + V286F. x=6 + V208

Answer 1

Given the polynomial:

`4x^2-6x+1`

We use the general formula for second degree equations

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

Where: a = 4, b = -6 and c = 1

`x_(1,2)=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot4\cdot1}}{2\cdot4}`

Simplify

`\begin{gathered} x_(1,2)=\frac{6\pm\sqrt[]{36-16}}{8} \\ x_(1,2)=\frac{6\pm\sqrt[]{20}}{8} \end{gathered}`

So, the roots are:

`\begin{gathered} x=\frac{6+\sqrt[]{20}}{8} \\ \text{and} \\ x=\frac{6-\sqrt[]{20}}{8} \end{gathered}`

Answer:

C and F