DSAT Advanced Math 3

Question 1

A polynomial p(x) satisfies p(2) = 0. Which of the following must be a factor of p(x)?

Accepted Answer

x - 2

Answer

By the Factor Theorem, if p(2) = 0, then (x - 2) is a factor of p(x).

Question 2

What is the sum of all solutions to x² - 5x + 6 = 0?

Accepted Answer

5

Answer

By Vieta's formulas, the sum of roots = -b/a = 5/1 = 5.

Question 3

Which of the following is equivalent to (x + 3)² - 4?

Accepted Answer

x² + 6x + 5

Answer

Expand (x+3)² - 4 = x² + 6x + 9 - 4 = x² + 6x + 5.

Question 4

For what value of k does the equation x² + kx + 16 = 0 have exactly one real solution?

Accepted Answer

8

Answer

For one solution the discriminant = 0: k² - 4(16) = 0 → k² = 64 → k = 8.

Question 5

The graph of y = a(x - h)² + k passes through (0, 5) with vertex at (2, 1). What is the value of a?

Accepted Answer

1

Answer

Substituting (0,5): 5 = a(0-2)² + 1 = 4a + 1, so 4a = 4 and a = 1.

(DSAT) Digital SAT Practice Test