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# Is There Any Real Value of 'A' for Which the Equation X2 + 2x + (A2 + 1) = 0 Has Real Roots? - Mathematics

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#### Question

Is there any real value of 'a' for which the equation x2 + 2x + (a2 + 1) = 0 has real roots?

#### 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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