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Quiz

Year 2: Equations of quadratic type and systems

10 questions with solutions for year 2: biquadratic equations, substitution, irrational equations, a system of one linear and one quadratic equation in two unknowns.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. How many real solutions does x⁴ − 5x² + 4 = 0 have?

2. The largest solution of x⁴ − 13x² + 36 = 0 is:

3. In (x² + x)² − 8(x² + x) + 12 = 0 put t = x² + x. What is t?

4. √(x + 3) = 4. x = ?

5. √(2x − 1) = x − 2. x = ?

6. The equation √(x − 1) = −2:

7. ∛(x + 2) = 2. x = ?

8. System: x + y = 5, x · y = 6. The solutions are:

9. System: y = x + 1, x² + y² = 25. What is x in the solution with positive coordinates?

10. How many solutions does the system y = x², y = 2x − 1 have?