Mathematics — Standard (041) — CBSE Class 10 board question

For $x^2 + x + 1 = 0$: $a=1,\ b=1,\ c=1$.

Discriminant $= b^2 - 4ac = 1 - 4 = -3 < 0$.

Since $b^2 - 4ac < 0$, the equation has no real roots.

Answer: (D) not-real

Source: Chapter 4, Section 4.4 – Nature of Roots

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The key tool here is the discriminant ($D = b^2 - 4ac$):

• $D > 0$ → two distinct real roots
• $D = 0$ → two equal real roots
• $D < 0$ → no real roots (not-real / complex roots)

Here $D = -3 < 0$, so the roots are not real. Always calculate the discriminant first for "nature of roots" questions.