Solving Quadratic Equations Flashcards

Solve x² = 49.

Answer: x = ±7

Taking the square root of both sides gives x = 7 or x = −7.

Which method is most efficient for solving x² − 9 = 0?

Answer: Difference of two squares

x² − 9 = (x − 3)(x + 3) = 0 is instantly solved as a difference of squares.

What value of k makes x² + kx + 16 = 0 have a repeated root?

Answer: 8

For a repeated root, discriminant = 0: k² − 64 = 0, so k = 8 (taking positive value).

Using the quadratic formula, solve x² − 3x − 10 = 0.

Answer: x = 5 and x = −2

x = (3 ± √49) / 2 = (3 ± 7) / 2, giving x = 5 or x = −2.

Solve 4x² − 1 = 0.

Answer: x = ±½

4x² = 1, x² = ¼, so x = ±½.

Complete the square to solve x² + 6x − 7 = 0.

Answer: x = 1 and x = −7

(x + 3)² − 16 = 0 → (x + 3)² = 16 → x = 1 or x = −7.

If one root of x² + bx + 12 = 0 is x = 3, what is the other root?

Answer: 4

By Vieta's formulas, the product of roots = 12, so the other root = 12/3 = 4.