The correct option is A The roots of the given equation are −2±i,2±√3i.
The equation is x4−4x2+8x+35=0. ...(1)
One root of this equation is given as 2+√3i.
Since the complex roots occur in conjugate pairs, the other root must be 2−√3i.
∴S=4,p=7The quadratic factor corresponding to these two roots is x2−Sx+P or x2−4x+7.
Then the other quadratic factor of L.H.S. of (1)
is of the form x2+px+5.
Hence we have the identity
Equating the coefficient of x on both sides of the above identity, we get 8=7p−20 or p=4.
[Note that same value of, will be obtained by equating the coefficient of x2].
Hence the other two roots of the equation are the roots of the equation x2+4x+5=0