Quadratic equation | ISI-B.stat | Objective Problem 240

The equations \(x^2 + x + a = 0\) and \(x^2 + ax + 1 = 0\)

Let the equations have a common root \(α\).Therefore \(α\) must satisfy two given equations.......

Therefore,

Now, \(α^2 + α + a = 0\)...................(1)
And, \(α^2 + aα + 1 = 0\).......................(2)

Can you find out the value of \(a\)?

Can you now finish the problem ..........

Therefore,

Using cross-multiplication betwwen (1) & (2) we will get.......

\(\frac{α^2}{(1 – a^2)} =\frac{ α}{(a – 1)} = \frac{1}{(a – 1)}\)
\(\Rightarrow {α}^2 = \frac{(1 – a^2)}{(a – 1) }=- (a + 1)\) & \(α=\frac{(a-1)}{(a-1)}=1\)

Now \({α}^2=(α)^2\)
\(\Rightarrow -(a+1)=1\)
\(\Rightarrow a = -2\)

Therefore (b) is the correct answer....

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