Elective Mathematics

Question 1

1Which is a factor of x³ − 6x² + 11x − 6?

Easy

A. x − 5 B. x − 1 C. x + 1 D. x + 2

Question 2

2Find the quotient when x² + 5x + 6 is divided by x + 2.

Easy

A. x + 3 B. x − 3 C. x + 6 D. x + 2

Question 3

3The equation x³ − 7x + 6 = 0 has roots

Hard

A. 1, 2, −3 B. 1, −2, 3 C. 1, 3, −2 D. −1, 2, 3

Question 4

4For 2x² − 8x + 3 = 0, what is the product of the roots?

Easy

A. 3/2 B. 4 C. 3 D. −4

Question 5

5If (x − 2) is a factor of x³ − 3x² + kx − 2, find k.

Medium

A. 1 B. −3 C. 3 D. 2

Question 6

6Find the remainder when x³ − 2x + 5 is divided by (x − 2).

Easy

A. 9 B. 5 C. 13 D. 1

Question 7

7For 2x² − 8x + 3 = 0, what is the sum of the roots?

Easy

A. −4 B. 4 C. 8 D. 3/2

Question 8

8The product of the roots of 2x² + 5x − 3 = 0 is

Easy

A. 3/2 B. 5/2 C. −5/2 D. −3/2

Question 9

9When f(x) is divided by (x − 1) the remainder is 3, and by (x + 1) it is −1. The remainder when divided by (x² − 1) is

Hard

A. 2x + 1 B. x + 2 C. 2x − 1 D. 3x − 1

Question 10

10If α, β and γ are roots of x³ − 6x² + 11x − 6 = 0, find α + β + γ.

Hard

A. −6 B. 1 C. 11 D. 6