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Question
If 2+i and √5−2i are the roots of the equation (x2+ax+b)(x2+cx+d)=0, where a,b,c,d are real constants, then product of all roots of the equation is
If 2+i and √5−2i are the roots of the equation (x2+ax+b)(x2+cx+d)=0, where a,b,c,d are real constants, then product of all roots of the equation is
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Solution
The correct option is C 45
Since, imaginary roots always appear in conjugate pairs when the coefficients are real.
2−i and √5+2i must be other roots of the equation.
Product of all roots
=(2+i)(2−i)(√5+2i)(√5−2i)
=(4−i2)(5−4i2)
=5×9
=45
Since, imaginary roots always appear in conjugate pairs when the coefficients are real.
2−i and √5+2i must be other roots of the equation.
Product of all roots
=(2+i)(2−i)(√5+2i)(√5−2i)
=(4−i2)(5−4i2)
=5×9
=45
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