Question 26

If $$a \in R$$, then the equation $$x^2 + x + a = 0$$ and $$x^2 + ax + 1 = 0$$ have a common real root for

Solution

Let '$$\alpha$$' be the common root which satisfies both the equations.
$$\alpha^{2}$$ + $$\alpha$$ + a = 0 and $$\alpha^{2}$$ + a$$\alpha$$ + 1 = 0
On subtracting the equations,
a($$\alpha$$ - 1) + 1- a=0
$$\alpha$$ = 1
Substitute the value of $$\alpha$$ in any of the equations, we get
a=-2

C is the correct answer.

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If $$a \in R$$, then the equation $$x^2 + x + a = 0$$ and $$x^2 + ax + 1 = 0$$ have a common real root for

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