Is it possible to factor $y = - x^{2} - 10 x + 20$ $y= - x^2 - 10x + 20$ ? If so, what are the factors?

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Answer 1 · 2015-12-26T12:32:19

It's possible to factor this polynomial in $RR$ as $-(x + 5 - 3sqrt5)(x + 5 + 3sqrt5)$

We need to calculate $Delta = b^2 - 4ac$ in order to find the roots.

Here, $Delta = 100 -4*(-1)*20 = 180 > 0$ so it has 2 real roots.

The quadratic formula tells us that the solutions are $(-b +- sqrtDelta)/2a$ . Here, $sqrtDelta = sqrt180 = 6sqrt5$

$x_1 = (10 - 6sqrt5)/-2 = (6sqrt5 - 10)/2 = 3sqrt5 - 5$ and $x_2 = (-10 - 6sqrt5)/2 = -5 - 3sqrt5$ .

Is it possible to factor y= - x^2 - 10x + 20y=−x2−10x+20y= - x^2 - 10x + 20? If so, what are the factors?