Question

the biquadratic equation two of whose roots are 1+i , 1-√2 is​

Answer 1

Answer:

Given one of the two roots is imaginary and the other is irrational.  

So, for the coefficients of the equation to be real and rational, the other two roots must be conjugates of these two roots.

Hence, the other two roots are 1−i and 1+  √2

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The quadratic equation with the two imaginary roots will be (x−1)²+1=0, and the quadratic equation with the two irrational roots will be (x−1)²−2=0.

Hence the required biquadratic equation will be the product of these two equations and will be

x^4−4x³+5x²−2x−2=0.