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