Question

Find the quadratic equation whose roots are -3+5i,-3-5i​

Answer 1

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Answer 2

Answer:

lets name your complex root as z , as we know that complex quadratic roots are always complex conjugate pairs

so the other root will be z' (assume apostrophe as bar )

so the required quadratic eqn would be

(x-z)(x-z')=0

⇒x²-(z+z')*x+z*z'=0

so put z=-3+5i and z'=-3-5i

⇒  x²-(-3+5i-3-5i)*x+(-3+5i)*(-3-5i)=0

then required quadratic eqn is

x²+6x+34=0