Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Start Practicing

Worksheet: Finding the Value of the Unknown Variable by Evaluating the Determinant

Q1:

Find the solution set of

  • A 1 4 , 1 4
  • B 0 , 1 4 , 1 4
  • C { 4 , 4 }
  • D { 0 , 4 , 4 }
  • E { 0 , 4 }

Q2:

Solve the determinant given that 0 < 𝜃 < 9 0 .

Q3:

Solve for 𝑥 :

  • A 𝑥 = 9 or 𝑥 = 2 0
  • B 𝑥 = 9 or 𝑥 = 4
  • C 𝑥 = 9 or 𝑥 = 2 0
  • D 𝑥 = 9 or 𝑥 = 4

Q4:

Find all the possible values of 𝑥 :

  • A 7 , 7
  • B 1 6 , 1 6
  • C 1 7 , 1 7
  • D 6 , 6
  • E 1 6

Q5:

Solve for 𝑥

  • A 1 6 , 8 7
  • B 1 7 , 4 3
  • C 8 7 , 1 6
  • D 4 3 , 1 7

Q6:

Solve for 𝑥 :

  • A 𝑥 = 0 , 𝑥 = 3 , or 𝑥 = 2 3
  • B 𝑥 = 1 , or 𝑥 = 3 2
  • C 𝑥 = 1 , 𝑥 = 3 2 , 𝑥 = 3 , or 𝑥 = 2 3
  • D 𝑥 = 0 , 𝑥 = 1 3 , 𝑥 = 1 , or 𝑥 = 2 3
  • E 𝑥 = 0 , 𝑥 = 3 , 𝑥 = 1 3 , or 𝑥 = 3 2

Q7:

Solve

  • A
  • B
  • C
  • D
  • E

Q8:

Find the solution set of in .

  • A { 1 }
  • B { 2 }
  • C { 3 }
  • D { 2 }

Q9:

Solve the equation

  • A 1 8
  • B { 8 }
  • C 1 8
  • D { 8 }

Q10:

Given that 𝑏 and 𝑐 are the roots of the equation 𝑥 1 2 𝑥 + 2 5 6 = 0 2 , determine the value of

Q11:

Solve the equation

  • A { 3 , 6 }
  • B { 2 , 9 }
  • C { 6 , 3 }
  • D { 9 , 2 }
  • E 5 3 3 , 4 6

Q12:

Solve the equation

  • A { 0 , 8 𝑎 + 𝑏 4 𝑐 }
  • B ± 8 𝑎 + 4 𝑐 , 8 𝑎 𝑏 4 𝑐
  • C ± 8 𝑎 + 4 𝑐 , 8 𝑎 + 𝑏 4 𝑐
  • D { 0 , 8 𝑎 𝑏 4 𝑐 }

Q13:

Consider the equation

How many distinct solutions does it have in the set of complex numbers?

Q14:

Determine the value of 𝑘 that makes 𝑥 = 4 a root of the equation

  • A 1 5
  • B5
  • C 3 2
  • D 1 2

Q15:

Find the solution set of the equation

  • A { 3 , 1 }
  • B { 3 , 1 , 0 }
  • C 1 3 , 1 , 0
  • D { 3 , 1 , 0 }

Q16:

Solve

  • A 𝑥 = 0 or 𝑥 = 1 5
  • B 𝑥 = 0 , 𝑥 = 4 , or 𝑥 = 5
  • C 𝑥 = 0 or 𝑥 = 1 5
  • D 𝑥 = 0 , 𝑥 = 4 , or 𝑥 = 5

Q17:

Solve the equation

  • A 7 3
  • B 7 𝑖 3 , 7 𝑖 3
  • C 7 𝑖 3
  • D 7 3 , 7 3

Q18:

Find the solution set of the equation | | | 𝑥 8 1 𝑥 + 9 𝑥 + 9 𝑥 8 1 | | | = 0 . 2 2

  • A { 8 , 9 , 1 0 }
  • B { 1 0 , 8 , 9 }
  • C { 1 0 , 9 , 8 }
  • D { 9 , 8 , 1 0 }
  • E { 9 , 9 }

Q19:

Find the solution set of the equation | | | 𝑥 9 𝑥 + 3 𝑥 + 3 𝑥 9 | | | = 0 . 2 2

  • A { 2 , 3 , 4 }
  • B { 4 , 2 , 3 }
  • C { 4 , 3 , 2 }
  • D { 3 , 2 , 4 }
  • E { 3 , 3 }

Q20:

Find the solution set of the equation

  • A { 2 , 3 }
  • B { 3 , 2 , 3 }
  • C { 3 , 2 }
  • D { 3 , 2 }
  • E { 2 , 3 }

Q21:

Find the solution set of the equation

  • A { 3 , 2 }
  • B { 0 , 2 , 3 }
  • C { 2 , 3 }
  • D { 0 , 3 , 2 }