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Question
Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?
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Solution
Let quadratic equation x2 + 2x + (a2 + 1) = 0has real roots.
Here, a = 1, b = 2 and ,c = (a2 + 1)
As we know that `D = b^2 - 4ac`
Putting the value of a = 1, b = 2 and ,c = (a2 + 1), we get
\[D = \left( 2 \right)^2 - 4 \times 1 \times \left( a^2 + 1 \right)\]
\[ = 4 - 4\left( a^2 + 1 \right)\]
\[ = - 4 a^2\]
The given equation will have equal roots, if D > 0
i.e.
\[- 4 a^2 > 0\]
\[ \Rightarrow a^2 < 0\]
which is not possible, as the square of any number is always positive.
Thus, No, there is no any real value of a for which the given equation has real roots.
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