Question
Sat March 12, 2011 By: Garima Srivastava

Given a quadratic equation , where a, b and c are real numbers. If 2+3i is one of the roots of the equation, what is the other root?Ans. In a quadratic equation with real coefficients, if the roots are complex then they always occur in complex conjugate pair. So, the other root is 2-3i

Expert Reply
Sat March 12, 2011
dear student,
pl note that the complex roots of a quadratic equation always occur in pairs, they are conjugates of each other.
so the other root is 2-3i
this happens because when you are solving the quadratic equation by using the quadratic formula there is a plus or minus sign before the radical sign right?
that radical is not real so comes out as something multiplied by i.
so once it becomes like 2+3i and when you take the negative sign the root is 2-3i
solving one question below to solve your doubt completely.
suppose the use of quad formula gives us
x=
so we see that both the roots have everything else the same except the sign between the two terms of the numerator.Hence when one root is given the other can be found easily by just changing the sign as mentioned above.
hope this clarifies your doubt.
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