Algebra Test Quadratic Equations 3

Question 1

What is the sum of the roots of x² - 7x + 10 = 0?

Accepted Answer

7

Answer

By Vieta's formulas, the sum of roots = -b/a = 7/1 = 7.

Question 2

Solve x² + 2x - 15 = 0 by factoring.

Accepted Answer

x = 3 and x = -5

Answer

Factor as (x + 5)(x - 3) = 0, giving x = 3 and x = -5.

Question 3

How many real solutions does x² + 1 = 0 have?

Accepted Answer

No real solutions

Answer

x² = -1 has no real solutions because a square cannot be negative.

Question 4

Which form of a quadratic is easiest for reading the roots directly?

Accepted Answer

Factored form

Answer

Factored form y = a(x - r₁)(x - r₂) directly shows the roots r₁ and r₂.

Question 5

What is the product of the roots of 2x² - 6x + 4 = 0?

Accepted Answer

2

Answer

By Vieta's formulas, the product of roots = c/a = 4/2 = 2.

Algebra Test Practice Test