InterviewSolution
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InterviewSolution
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The value of `b` for which the equation `x^2+bx-1=0 and x^2+x+b=0` have one root in common isA. `-sqrt2`B. `-isqrt3`C. `I sqrt5`D. `sqrt2` |
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Answer» Correct Answer - B If `a_(1)x^(2)+b_(1)x+c_(2)=0` have a common real roots, then `implies(a_(1)c_(2)-a_(2)c_(1))^(2)=(b_(1)c_(2)-b_(2)c_(1))(a_(1)b_(2)-a_(2)b_(1))` `therefore{:(x^(2)+bx-1=0),(x^(2)+x+b=0):}` have a common root. `implies(a+b)^(2)=(b^(2)+1)(1-b)` `implies b^(2)+2b+1=b^(2)-b^(3)+1-b` `impliesb^(3)+3b=0` `thereforeb(b^(2)+3)=0` `impliesb=0, pmsqrt3i` |
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