Form the quadratic equation whose roots are $-3 \pm 5i$.

Form the quadratic equation whose roots are -3 ± 5i.

Question 7 of 13

-3 \pm 5i

Yanam BieapBIEAP Intermediate Board 2023Subjective· 2mImportance★★★★★

54% · 7/13 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

For roots $\alpha,\beta$ the required equation is $x^2-(\alpha+\beta)x+\alpha\beta=0$ ; compute the sum and product of $-3\pm5i$ .

Let $\alpha=-3+5i$ and $\beta=-3-5i$ (a conjugate pair, since a quadratic with real coefficients has complex roots occurring in conjugate pairs).

Sum: $\alpha+\beta = (-3+5i)+(-3-5i) = -6$ .

…