Question

$x {}^{2} - 20x + 120 = 0$
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Answer 1

Answer:

Imaginary roots

Step-by-step explanation:

$x^2 - 20x + 120 = 0\\\\\\\therefore \: x = \dfrac{20 \pm \sqrt{400 - 480}}{2}\\\\\\\text{Here, Since the discriminant is negative, ie, less than zero,}\\\text{Its roots are imaginary and not real.}$

Answer 2

$\mathfrak{Answer:-}\\ \texttt 10+2\sqrt5\ and\ 1-2\sqrt5$

Step-by-step explanation:

$\rm In\ this\ question,\ we've\ to\ find\ the\ answer\ for\ the\ equation\ x^2-20x+120=0\\ \\ \rm Here,\ a=1,\ b=(-20)\ and\ c=120\\ \rm Before\ finding\ the\ answer\ directly,\ lets\ find\ its\ discriminant.\\ \\ \rm Formula\ is\ \bf \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ \rm Putting\ values\ in\ the\ formula\\ \\ \rm \frac{-(-20)\pm\sqrt{400-4×120}}{2\times 1}\\ \\ \implies \rm \frac{20\pm \sqrt{400-480}}{2}\\ \\ \implies \rm \frac{20\pm\sqrt{-80}}{2}\\ \\ \implies \rm \frac{20\pm 4\sqrt5}{2}\\ \\ \implies \rm 10\pm 2\sqrt5\\ \implies \rm 10+2\sqrt5\quad or\quad 10-2\sqrt5\\ \rm \therefore The\ roots\ of\ the\ equation\ are\ \bf 10+2\sqrt5\quad and\quad 10-2\sqrt5\ \rm and\ are\ imaginary.$