Solving Quadratic Equations Flashcards

Solve 3x² − 12 = 0.

Answer: x = ±2

3x² = 12, x² = 4, so x = ±2.

Which of these quadratics cannot be solved by factoring over integers?

Answer: x² + x + 1 = 0

x² + x + 1 has discriminant = 1 − 4 = −3, so it has no integer factors.

The sum of a number and its square is 12. Which equation models this?

Answer: x² + x − 12 = 0

x + x² = 12 rearranges to x² + x − 12 = 0.

What are the x-intercepts of the graph of y = x² − x − 6?

Answer: (3, 0) and (−2, 0)

Setting y = 0: (x − 3)(x + 2) = 0 gives x = 3 or x = −2.

Solve 5x² + 5x = 0.

Answer: x = 0 and x = −1

Factor as 5x(x + 1) = 0, giving x = 0 or x = −1.

Using completing the square, what is the solution to x² − 8x + 7 = 0?

Answer: x = 1 and x = 7

(x − 4)² − 9 = 0 → x − 4 = ±3 → x = 7 or x = 1.

A ball is thrown upward and its height in metres is h = −5t² + 20t. At what times is the ball at ground level (h = 0)?

Answer: t = 0 and t = 4

−5t(t − 4) = 0 gives t = 0 (launch) and t = 4 seconds (landing).