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Find a quadratic equation with integral coefficients having the given roots i√ 5 , -i√ 5

The two factors associated with this equation are

z- i√ 5 and z -(- i√ 5) = z + i√ 5 .

Hence, the required equation is simply given by

(z- i√ 5)(z + i√ 5) = 0

z^2 - (i√ 5)^2 = 0 (Note the expansion (a-b)(a+b)=a^2-b^2 is used here)

Since i^2 = -1 (i is the imaginary number = √ -1 )

the above reduces to

z^2 + 5 = 0 (shown)

Hope this helps. Peace.

Algebra

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