Quadratic equations hard

Quadratic Equations Quiz (Hard)

1. What is the discriminant (b^2 - 4ac) of a quadratic equation used for?

a) To find the value of 'x' b) To determine the nature of roots c) To find the vertex

2. For a quadratic equation ax^2 + bx + c = 0, what is the sum of the roots when 'b' is negative?

a) -b/a b) b/a c) -2c/a

3. For a quadratic equation ax^2 + bx + c = 0, what is the product of the roots when 'c' is negative?

a) -c/a b) c/a c) -b/a

4. What is the nature of roots for a quadratic equation ax^2 + bx + c = 0 when 'b^2 - 4ac' is positive?

a) Real and distinct roots b) Real and equal roots c) Complex roots

5. What is the nature of roots for a quadratic equation ax^2 + bx + c = 0 when 'b^2 - 4ac' is zero?

a) Real and distinct roots b) Real and equal roots c) Complex roots

6. What is the nature of roots for a quadratic equation ax^2 + bx + c = 0 when 'b^2 - 4ac' is negative?

a) Real and distinct roots b) Real and equal roots c) Complex roots

7. For a quadratic equation ax^2 + bx + c = 0, what is the condition for having real and distinct roots?

a) b^2 - 4ac > 0 b) b^2 - 4ac = 0 c) b^2 - 4ac < 0

8. For a quadratic equation ax^2 + bx + c = 0, what is the condition for having real and equal roots?

a) b^2 - 4ac > 0 b) b^2 - 4ac = 0 c) b^2 - 4ac < 0

9. For a quadratic equation ax^2 + bx + c = 0, what is the condition for having complex roots?

a) b^2 - 4ac > 0 b) b^2 - 4ac = 0 c) b^2 - 4ac < 0

10. What is the formula to find the value of 'x' in a quadratic equation ax^2 + bx + c = 0?

a) x = (-b ± √(b^2 - 4ac)) / 2a b) x = -b / 2a c) x = √(b^2 - 4ac) / 2a