#### Question

In the following, determine whether the given quadratic equation have real roots and if so, find the roots:

*x*^{2} + *x* + 2 = 0

#### Solution

We have been given, *x*^{2} + *x* + 2 = 0

Now we also know that for an equation ax^{2} + bx + c = 0, the discriminant is given by the following equation:

D = b^{2} - 4ac

Now, according to the equation given to us, we have,a = 1, b = 1 and c = 2.

Therefore, the discriminant is given as,

D = (1)^{2} - 4(1)(2)

= 1 - 8

= -7

Since, in order for a quadratic equation to have real roots, D ≥ 0.Here we find that the equation does not satisfies this condition, hence it does not have real roots.

Is there an error in this question or solution?

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In the Following, Determine Whether the Given Quadratic Equation Have Real Roots and If So, Find the Roots: X2 + X + 2 = 0 Concept: Relationship Between Discriminant and Nature of Roots.

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