Question

Which two values of x are roots of the polynomial below?
4x2-6x+1

Answer 1

The roots of quadratic equation are $\frac{-6+ \sqrt{20}}{8}$ and $\frac{-6- \sqrt{20}}{8}$

The roots of quadratic equation $ax^{2} +bx+c$ is given as,

                         $x=\frac{-b\pm \sqrt{b^{2}-4ac } }{2a}$

Given equation is,

                              $4x^{2} -6x+1$

Substituting all values after comparison in above formulas,

                 $x=\frac{-6\pm \sqrt{36-16} }{8} \\\\x=\frac{-6\pm \sqrt{20}}{8}$

Hence, the roots of quadratic equation are $\frac{-6+ \sqrt{20}}{8}$ and $\frac{-6- \sqrt{20}}{8}$

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