Thread: third-degree polynomial with real coefficients

1. third-degree polynomial with real coefficients

find a third-degree polynomial with real coefficients and with zeros -3 +i and -4 are zeros

2. Re: third-degree polynomial with real coefficients

Hello, yuppie!

Find a third-degree polynomial with real coefficients and with zeros $-3 +i$ and $-4.$

Complex roots always appear in conjugate pairs.
Hence, if $-3+i$ is a root, then $-3-i$ is also a root.

The cubic is: . $\big(x - [-4]\big)\,\big(x - [-3+i]\big)\,\big(x - [-3-i]\big)$

. . . . . . . . $=\;(x+4)(x+3-i)(x+3+i)$

. . . . . . . . $=\;(x+4)(x^2+6x+10)$

. . . . . . . . $=\;x^3 + 10x^2 + 34x + 40$