How many roots?

Algebra Level 2

What can you say about the roots of the polynomial $x^2 - 6x + 2$ ?

No real roots Exactly two positive roots Just one real root Exactly two negative roots

1 solution

Janardhanan Sivaramakrishnan
Dec 14, 2015

The roots are $\frac{6 \pm \sqrt{(-6)^2-4\times 2}}{2}=3 \pm \sqrt{7}$ . The smaller root $3-\sqrt{7}$ is also positive as $3^3>7$