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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The value(s) of $b$ for which the equations
$x^2+bx-1=0$ and $x^2+x+b=0$ have one root in common is/are:
Solution
Let common root be $r$. Then $r^2+br-1=0$ and $r^2+r+b=0$. Subtract: $r(1-b)+(b+1)=0\Rightarrow r=\dfrac{b+1}{b-1}$ (for $b\ne1$). Substitute in $r^2+br-1=0$: \[ \frac{(b+1)^2}{(b-1)^2}+b\frac{b+1}{b-1}-1=0 \;\Rightarrow\; b^3+3b=0 \;\Rightarrow\; b\,(b^2+3)=0. \] Hence $b=0$ or $b=\pm i\sqrt3$.Online Test Series, Information About Examination,
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