Quadratic Equations — Important Questions

2x² + 3x - 1 = 0, x² - 7 = 0, 4x² = 9

A quadratic equation has the form ax² + bx + c = 0 where a ≠ 0. Options 1, 3, and 5 are quadratic equations. Option 2 is cubic (degree 3), and option 4 is linear (degree 1).

Factorization, Quadratic formula, Completing the square, Square root method

The four main methods to solve quadratic equations are: factorization, quadratic formula, completing the square, and square root method (for equations of the form x² = k).

x = 3 (repeated root)

This is a perfect square: x² - 6x + 9 = (x - 3)² = 0. Therefore, x - 3 = 0, giving x = 3 (repeated twice). This is also called equal roots.

-5/2

For a quadratic equation ax² + bx + c = 0, sum of roots = -b/a. Here a = 2, b = 5, so sum = -5/2.