Common Core HSA.REI.B.4.B worksheet

Question 1

For which values of k does x² + 2x + k = 0 have no real roots?

• A. k > −1
• B. k > 1
• C. k < 1
• D. k = 1

Question 2

x² + kx + 64 = 0 has equal roots and k is positive. Find k.

Answer 

Question 3

Solve x² + 2x − 26 = 0 with the quadratic formula. Simplify fully.

• A. x = −1 ± 6√3
• B. x = 1 ± 3√3
• C. x = −1 ± 3√3
• D. x = −1 ± √27/2

Question 4

Solve x² + 8x − 14 = 0 by completing the square. Give exact answers.

• A. x = −8 ± √30
• B. x = −4 ± √46
• C. x = −4 ± √30
• D. x = −4 ± 30

Question 5

Solve: (x − 7)(x + 7) = 0. Give both solutions, separated by a comma.

x = 

Question 6

Solve: x² − 8x = 0. Give both solutions, separated by a comma.

x = 

Question 7

Work out the discriminant of 5x² − 8x + 1 = 0.

Answer 

Question 8

How many real solutions does 4x² − 8x − 9 = 0 have?

• A. Two
• B. One (repeated)
• C. None

Question 9

Solve: x² − 5x + 6 = 0. Give both solutions, separated by a comma.

x = 

Question 10

Solve 3x² + 7x − 7 = 0 using the quadratic formula. Give the smaller solution to 2 decimal places.

Answer 

Question 11

Solve (x + 2)² = 6, giving exact answers.

• A. x = −2 + √6
• B. x = −2 ± 6
• C. x = −2 ± √6
• D. x = ±√10

Question 12

Rewrite x² + 8x + 8 = 0 as (x + 4)² = k. Find k.

Answer 

Question 13

Solve: (x − 4)² = 16. Give both solutions, separated by a comma.

x = 

Question 14

Solve x² − 8x − 2 = 0. Give exact answers in the form (p ± √q)/r.

• A. x = (8 ± √56)/2
• B. x = 8 ± √72/2
• C. x = (8 ± √72)/2
• D. x = (−8 ± √72)/2

Question 15

Solve: x² + 9 = 13. Give both solutions, separated by a comma.

x = 

Question 16

Which method is the most efficient way to solve (x − 4)² = 29?

• A. Take square roots
• B. Factorise
• C. Use the quadratic formula