Question

.. Discuss the nature of the root of equation x2 + 2x + 3 = 0​

Answer 1

• No real roots

Explanation:

Given equation:

• x² + 2x + 3 = 0

On comparing the equation by ax² + bx + x = 0, We get: a = 1, b = 2 and c = 3

To Find the nature of the roots of the equation firstly we need to find the discriminant of the equation. The expression b²- 4ac is called the discriminant.

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• Two Distinct real roots, if b² - 4ac > 0
• Two equal real roots, if b² - 4ac = 0
• No real roots, if b² - 4ac < 0

`\\ \: \: \dashrightarrow \: \: \: \sf {b}^(2) - 4ac = 0 \\ \\ \\\: \: \dashrightarrow \: \: \: \sf (2)² - 4 * 1 * 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 4 * 1 * 3 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf 4 - 12 = 0 \\ \\ \\ \: \: \dashrightarrow \: \: \: \sf {\underline{\boxed{\sf{\purple{ -8 > 0}}}}} \\ \\`

The discriminant is smaller than 0.

• Hence, Equation has no real roots (no solution)