A value of b for which the equations x2 + bx – 1 = 0 x2 + x + b = 0 have one root in common is

Engineering

Mathematics

Condition for Common Roots

Question

A value of b for which the equations

x² + bx – 1 = 0

x² + x + b = 0

have one root in common is

$\sqrt{2}$

$i \sqrt{5}$

$- \sqrt{2}$

$- i \sqrt{3}$

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x² + bx – 1 = 0 …………(i)

x² + x + b = 0 …………(ii)

(i) – (ii) we get $x = \frac{b + 1}{b - 1}$

Put this value in (i)

${(\frac{b + 1}{b - 1})}^{2} + b (\frac{b + 1}{b - 1}) - 1 = 0$

$\Rightarrow$ b² + 3b = 0

$\Rightarrow$ b(b² + 3) = 0

$\Rightarrow$ b = 0 or b = ± i $\sqrt{3}$